Question

Given R vector = A vector+ B vector and R= A=B. The angle between A and
B is...??​

Answer 1

Answer:

120° is the right answer.

Explanation:

R = A + B = √A^2 + B^2 + 2AB cos theta

if A, B are same.

then

R = A + B

R = √2A^2 + 2A^2 cos theta

for getting R=A

theta have to be 120°.

cos 120°=-1/2

putting values

R = √2A^2 - A^2

R = √A^2

R =A

and

A=B (Given)

so, R=A=B

Hence, Proved.

Answer 2

The angle between A & B is 120°.

Given:

• $vec{R}=\vec{A}+\vec{B}$
• R = A = B

To find:

• Angle between A and B ?

Calculation:

$\vec{R}=\vec{A}+\vec{B}$

$\implies \: | \vec{R}| = \sqrt{ {A}^{2} + {B}^{2} + 2.A.B . \cos( \theta) }$

• Let $\theta$ be the angle between A and B.

• As per the question, R = A = B = x (let)

$\implies \: x = \sqrt{ {x}^{2} + {x}^{2} + 2.x.x . \cos( \theta) }$

$\implies \: x = \sqrt{ 2 {x}^{2} + 2 {x}^{2} \cos( \theta) }$

• Squaring both sides:

$\implies \: {x}^{2} = 2 {x}^{2} + 2 {x}^{2} \cos( \theta)$

$\implies \: 2 {x}^{2} \cos( \theta) = - {x}^{2}$

$\implies \: 2 \cos( \theta) = - 1$

$\implies \: \cos( \theta) = - 0.5$

$\implies \: \theta = {120}^{ \circ}$

So, angle between A and B is 120°.