Answers
Answer:
[tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex] if and only if [tex]\vec{B}[/tex] is a zero vector.
Explanation:
An equation is true if and only if adding the same value to both sides of the equation (the value needs to be compatible) gives an equation that is also true.
Start with the [tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex].
This equation is true if and only if [tex]\left(\vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B}[/tex] ([tex]\vec{B}[/tex] is added to both sides of the original equation.)
Vector addition and subtraction are associative. Therefore, [tex]\left(\vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B}[/tex] if and only if [tex]\vec{A} + \left(\vec{B} + \vec{B}\right) = \vec{A} + \left(- \vec{B} + \vec{B}\right)[/tex], which is equivalent to [tex]\vec{A} + 2\, \vec{B} = \vec{A}[/tex].
[tex]\vec{A} + 2\, \vec{B} = \vec{A}[/tex] if and only if [tex]\left(-\vec{A}\right) + \vec{A} + 2\, \vec{B} = \left(-\vec{A}\right) + \vec{A}[/tex] ([tex]\left(-\vec{A}\right)[/tex]is added to both sides of this equation,) which is equivalent to [tex]2\, \vec{B} = \vec{0}[/tex].
[tex]2\, \vec{B} = \vec{0}[/tex] if and only [tex]\displaystyle \frac{1}{2} \cdot \left(2\, \vec{B}\right) = \frac{1}{2} \cdot \vec{0}[/tex], which is equivalent to [tex]\vec{B} = \vec{0}[/tex]. That is: [tex]\vec{B}[/tex] is the zero vector.
In other words:
[tex]\begin{aligned}& \vec{A} + \vec{B} = \vec{A} - \vec{B}\\ &\iff \left( \vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B} \\ &\iff \vec{A} + \left(\vec{B} + \vec{B}\right) = \vec{A} + \left(- \vec{B} + \vec{B}\right) \\ & \iff \vec{A} + 2\, \vec{B} = \vec{A} \\ & \iff \left(-\vec{A}\right) + \vec{A} + 2\, \vec{B} = \left(-\vec{A}\right) + \vec{A} \\ &\iff 2\, \vec{B} = \vec{0} \\ &\iff \frac{1}{2} \cdot 2\,\vec{B} = \frac{1}{2} \cdot \vec{0} \\ &\iff \vec{B} = \vec{0}\end{aligned}[/tex].
Hence, [tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex] if and only if [tex]\vec{B}[/tex] is the zero vector.
Related Questions
How many lobes are in the lungs
Answers
Answer:
There are 5 lobes in the lungs.
Explanation:
The right lung consists of three lobes: the RUL, the RML, and the RLL. While the left lung consists of two lobes: the LUL, and the LLL.
The oxygen side of a water molecule is
Answers
A cyclist rides at 6.20 m/s through a intersection. A stationary car begins to
accelerate at 3.844 m/s2 when the bike is beside it. They reach the other side of
the intersection at the same time. Find the width of the intersection.
Answers
Answer:
The width of the intersection is 20 meters
Explanation:
The speed with which the cyclist is riding, v₁ = 6.20 m/s
The rate at which the car starts to accelerate, a = 3.844 m/s²
The initial velocity of the car = The car is stationary at the start = 0 m/s
The time at which the cyclist and the car reach the other side of the intersection = The same time;
Let 't' represent the time at which the cyclist and the car both reach the other side of the intersection, we have;
The distance travelled by the cyclist = The distance traveled by the car
∴ v₁ × t = 1/2 × a × t²
Plugging in the values for 'v₁', and 'a' in the above equation, we get;
6.20 × t = 1/2 × 3.844 × t²
∴ 1.922·t² - 6.20·t = 0
∴ t·(1.922·t - 6.20) = 0
t = 0, or t = 6.20/1.922 = 100/31
The time at which the cyclist and the car both reach the other side of the intersection, t = 100/31 seconds
The with of the intersection, w = v₁ × t
∴ w = 6.20 × 100/31 = 100/5 = 20
The width of the intersection, w = 20 meters.
By the end of the 19th century, more than half of the population believed in the presence of atoms.
Answers
Answer:
hello your question is vague hence I will provide a general answer about what was known about atoms in the 19th Century
answer :
By the end of the 19th century more than half of the population believed in the presence of atoms and also in the 19th Century is was a known fact that atoms determine the chemical properties of an element
Explanation:
By the end of the 19th century more than half of the population believed in the presence of atoms and also by the 19th Century is was a known fact that atoms determine the chemical properties of an element.
John Dalton reintroduced the presence of atoms in 1800 with evidence which he used to develop atomic theory. with this theory people believed in the presence of atoms in nature and also that atoms determine the chemical properties of an element .
Which three parts of the graph’s curve represent the solid, liquid, and gaseous state of water? Explain your reasoning.
Answers
B,C,D maybe
Explanation:
plz dont get mad
Metals allow electrons to flow through and complete the circuit. Therefore they are called?
Answers
Answer:
the answer would be conductors
PLEASE HELP ME ASAP!!!
Answers
Answer:
90
Explanation:
The portion where gas turns to liquid
which diagram represents the greatest magnitude of displacement for an object
Answers
Answer: if every arrow=1m do 1 times 1 times 1 times 1
Explanation:
(p.s. it equals 1 meter in area 4 meters in perimeter)
half life, for my physics but pretty sure it involves maths. you don’t have to do them all i’m just confused how to work it out.
Answers
I probably don't have to tell you that the other answer is nonsense, but I'll do it all the same, just in case... Half-life is defined as the time it takes for some radioactive substance to decay to half its original amount.
If it takes n half-lives for some substance with a starting amount of A to decay to a final amount of B, then
[tex]B = \dfrac{A}{2^n}[/tex]
1. If the half-life is x, then after 1 half-life, 5000 units of this substance decays to 2500 units. After another half-life, this decays to 1250. After another, this in turn decays to 625.
So 3 half-lives are required.
In terms of the equation above, we solve for n such that
[tex]625 = \dfrac{5000}{2^n} \implies 2^n = 8 \implies n=3[/tex]
since 2³ = 8.
2. Count how many times you halve 15,000 to end up with 3750:
15,000/2 = 7500
7500/2 = 3750
===> 2 half-lives
In other words,
[tex]3750 = \dfrac{15,000}{2^n} \implies 2^n = 4 \implies n=2[/tex]
3. After 1 half-life, you would end up with
12,000/2 = 6000
and after another half-life,
6000/2 = 3000
i.e.
[tex]\dfrac{12,000}{2^2} = \dfrac{12,000}4 = 3000[/tex]
4. After 1 half-life, you have
26,000/2 = 13,000
After 2 half-lives,
13,000/2 = 6500
After 3 half-lives,
6500/2 = 3250
After 4 half-lives,
3250/2 = 1625
i.e.
[tex]\dfrac{26,000}{2^4} = \dfrac{26,000}{16} = 1625[/tex]
5. If the half-life is 3 years, then 15 years = 3 half-lives.
In the last 3 years, 20,000 would have decayed to 10,000.
In the second-to-last 3 years, 40,000 would have decayed to 20,000.
In the first 3 years, 80,000 would have decayed to 40,000.
i.e.
[tex]\dfrac{x}{2^3} = 10,000 \implies x = 8\times10,000 = 80,000[/tex]
Use the graph. Which time period was
the car moving the fastest?
Answers
Answer:
1,2,3,4
Explanation:
Joey's little brother makes a ramp to push hos toy dump truck up to his sandbox. if he uses 5N of force to push the 12N truck up the ramp, what is the mechanical advantage of his ramp?
A. 6.0
B.0.42
C. 2.4
D. 23.5
Answers
Rank the ten objects from loudest to softest.
Answers
If the maximum moment of force on a door is 10 Nm by an applied force of 2.25 N, then the distance of handle
Answers
Answer:
d = 4.44 m
Explanation:
Given that,
The moment of force on a door = 10 N-m
The applied force, F = 2.25 N
We need to find the distance of the handle. The moment of force is given by :
[tex]\tau=F\times r[/tex]
Where
r is the distance of the handle.
[tex]r=\dfrac{\tau}{F}\\\\r=\dfrac{10}{2.25}\\\\r=4.44\ m[/tex]
So, the required distance is equal to 4.44 m.
___________containing powerful telescopes have been built throughout the world to study features of stars, galaxies, planets, and other objects in the sky
a
heliocentric model
b
Space Station
c
star chart
d
Observatories
WILL GIVE BRAINLIEST
Answers
Explanation: There are a few keywords like built. Plus star charts contain features of stars, galaxies, planets, and other objects in the sky
What distance separates Earth and the Sun? A 300,000 km per second B Eight light-minutes C 149 million light-seconds D One light-year
Answers
Answer:
B Eight light-minutes
Explanation:
In the case when the distance separated earth and the sun so here we orbit the sun for a 150 million km distance and the light moves would be 300,000 kilometers per second
Now divide this
= 150 million ÷ 300,000 kilometers per second
= 500 seconds
This 500 seconds represent 8 minutes and 20 seconds
Hence, option B is correct
Answer:
B) Eight light-minutes
Question 19 (4 points) A 2-kg ball traveling in the y-direction (North) collides with a 6-kg ball, initially at rest. After the collision, the 6-kg ball is moving at 5 m/s, 53° West of North. The 2-kg ball is moving 37° East of North. 6 kg 530 5 m/s 379 VE 2 kg before 6 kg after 2 kg What was the initial speed of the small ball (before the collision)? 20 m/s 35 m/s 30 m/s 15 m/s 40 m/s 10 m/s 25 m/s
Answers
An observer in the Northern Hemisphere watches the sky for several hours. Due to the motion of Earth, this observer notices that the stars near the north celestial pole appear to move An observer in the Northern Hemisphere watches the sky for several hours. Due to the motion of Earth, this observer notices that the stars near the north celestial pole appear to move from left to right. nearly vertically upward. counter-clockwise around the celestial pole. from right to left.
Answers
Answer:
counter clockwise
Explanation:
The observer in the Northern Hemisphere will notice that the stars near the NCP to move counter-clockwise
Counter - clockwise : The observer will observe this because the earth movement when viewed from the North pole is in a counterclockwise direction, hence the stars will appear to move in an ant-clockwise direction
whar determines the direction of ocean currents
Answers
Answer:
The direction in which they rotate is determined by the hemisphere in which they are located. The main overall global wind patterns, the rotation of the Earth, and the shape of ocean basins are the three major factors that decide surface currents.
Oceanic factors are Tempature, salinity, density, pressure gradient and melting of ice. Atsmopheric factors are atsmopheric pressure, winds, rainfall, evaporation and insolation
Which statement compares the attractive forces that hold particles together?
A. Covalent bonding and Van der Waals forces join separate
molecules together, while ionic and hydrogen bonding produce
compounds.
B. Covalent and hydrogen bonding produce compounds, while ionic
bonding and Van der Waals forces join separate molecules
together.
C. lonic and covalent bonding produce compounds, while hydrogen
bonding and Van der Waals forces join separate molecules
together.
D. Ionic and covalent bonding join separate molecules together, while
hydrogen bonding and Van der Waals forces produce compounds.
Answers
Answer:
Ionic and covalent bonding produce compounds, while hydrogen bonding and Van der Waals forces join separate molecules together.
Ur welcome:)
Answer:
C) lonic and covalent bonding produce compounds, while hydrogen bonding and Van der Waals forces join separate molecules together.
Explanation:
Please help me fr fr !
Answers
Answer:
Explanation:
Which part of and organism is preserved in cast and mold fossils
Answers
Answer:
bones
Explanation:
Bones are is preserved in cast and mold fossils.
Normally the other 'parts of the body' like muscles, ligaments, blood and organs are soft.
Answer:
bones
Explanation:
Which two statements best explains how observations of the spectra of light from galaxies are used to support current theories of the origin and evolution of the universe?
A: Galaxies that are further away tend to have larger redshifts
B: the blueshift observed from distant galaxies indicate that galaxies remain stationary relative to earth
C: the redshift observed from nearby galaxies indicates that most galaxies remain stationary relative to earth
D: the blueshift observed from nearby galaxies indicates that the solar system is orbiting a black hole
E: the redshift observed from distant galaxies indicates that they are moving away faster than nearby galaxies
Answers
What happens when cooler downdrafts inside a supercell move across the edge of an upward moving mesocyclone?
A. A supercell
B. A me so cyclone
C. A tornado
D. A hurricane
Answers
there is T__ as much voltage. This
produces twice the current
Answers
A hockey puck slides across the ice with an initial velocity of 7.3 m/s .It has a decleration of 1.1 m/s and is traveling towards the goal 5.0 m away .How much time does the goalie have to stop the puck?
Answers
Answer:
t = 6.63 s
Explanation:
Given that,
Initial velocity of the puck, u = 7.3 m/s
Deacceleration of the puck, a = -1.1 m/s²
Distance traveled, d = 5 m
We need to find the time the goalie have to stop the puck. Using equation of motion.
v = u +at
v = 0 (stops)
So,
[tex]u=-at\\\\t=\dfrac{u}{-a}\\\\t=\dfrac{7.3}{-(-1.1)}\\\\t=6.63\ s[/tex]
So, the required time is 6.63 seconds.
If a motorcycle, a car, and a big rig are all moving with a velocity of 100 km/h, which vehicle has the greatest momentum? A motorcycle and rider. A small car. A large 18 wheeler truck.
Answers
Answer:
The big rig.
Explanation:
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
[tex] Momentum = mass * velocity [/tex]
In this scenario, a motorcycle, a car, and a big rig are all moving with a velocity of 100 km/h. Thus, the vehicle which has the greatest momentum is the big rig because its mass is intuitively or logically greater than that of the other vehicle.
Generally, momentum is directly proportional to the mass of a physical object or body.
Answer: A large 18 wheeler truck.
Explanation: Momentum is the measure of the motion of an object found by multiplying the object’s mass and velocity. Momentum is directly proportional to the object's mass and also its velocity. So, the greater an object's mass or the greater its velocity, the greater its momentum. Therefore, since the truck is bigger, it has the greatest mass. This means that the truck the greatest momentum. Correct on Edg 2020.
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What kind of energy involves the flow of positive charges?
thermal
radiant
electrical
nuclear
Answers
Electrical would be the energy that involves the flow of positive changes
Answer:
Electrical
Explanation:
Electrical would be the energy that involves the flow of positive charges.
the girl has a weight of 72N on moon.what will be the mass and the weight of the girl on earth.(use g earth=10m/s 2/g 9 moon=1.6m/s 2)
Answers
Answer:
F(m)= mg(m)
m=F(m)/g(m)=72/1.6=45kg
F(e)= mg(e)= 45 x 10 m/s= 450N
plz help me
Your friend has a mass of 70 kg and is running at a velocity of 3 m/s. What is their kinetic energy?
Answers
Answer:
TINAAA
Explanation:
Use the drop-down menus to identify the order of these images for the formation of our solar system. A collapsed nebula flattens into a disc. A collapsed solar nebula. An image of our solar system. nebula. An image of our solar system.
Answers
Answer: 2 1 3
is your answer
Explanation:
your'e welcome
Answer:
First one = 2
Second one = 1
Third one = 3
Explanation:
2 1 3
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