Question

Given that; A = B = C. If A bar+B bar=C bar, then angle between A bar And C bar is theta 1 .If A bar+ B bar+C bar= 0, then the angle between A bar and C bar is theta 2. What is the relation between theta1 and theta2?

Answer 1

Answer:

plzzz give me brainliest ans and plzzzz follow me

Answer 2

Answer:

the relation between the angles is $\theta_{1} =\theta_{2}$.

Explanation:

Given magnitude of vectors, $A = B = C$                                          ...(1)

When $\vec A + \vec B = \vec C$, then the angle between $\vec A$ and $\vec C$ is $\theta_{1}$.              ...(2)

When $\vec A + \vec B + \vec C=0$, then the angle between $\vec A$ and $\vec C$ is $\theta_{2}$.       ...(3)

From the second condition,

$\vec A + \vec B = \vec C$

squaring on both sides,

$(\vec A + \vec B)^{2} =(\vec C)^{2}$

$\implies (\vec A )^{2} +2(\vec A . \vec B)+ ( \vec B)^{2} =(\vec C)^{2}$

$\implies A ^{2} +2 A Bcos\theta_{1}+B^{2} = C^{2}$

Using condition (1),

$\implies A ^{2} +2 A Acos\theta_{1}+A^{2} = A^{2}$

$\implies 2 A^{2} cos\theta_{1}+A^{2} =0$

$\implies cos\theta_{1} =-\frac{1}{2}$

$\implies \theta_{1} =120^{o}$

From the third condition,

$\vec A + \vec B = -\vec C$

squaring on both sides,

$(\vec A + \vec B)^{2} =(\vec C)^{2}$

As it is similar to the previous equation,

$\theta_{2} =120^{o}$

Therefore, the relation between the angles is $\theta_{1} =\theta_{2}$.