Question

The vectors A and B are such that
A+B| = |A-B). The angle between vectors A
and B is -​

Answer 1

Answer:

90°

Explanation:

Given

$|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$

Now

According to Question

$|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}| \\ = > \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos \theta } = \\ \sqrt{ {a}^{2} + {b}^{2} - 2ab \cos \theta }$

On Cancelling Square Root Both Sides

$= > { \cancel{A}^{2}} + { \cancel{B}}^{2} + 2AB \cos \theta = \\ { \cancel{A}}^{2} + { \cancel{B}}^{2} - 2AB \cos \theta$

$= > 2AB \cos \theta = - 2AB \cos \theta \\ = > 2AB \cos \theta + 2AB \cos \theta = 0$

$= > 4AB \cos \theta = 0 \\ = > \cos \theta = \frac{0}{4AB}$

We Know when O is divided by anything it becomes 0.

So

$= > \cos \theta = 0 \\ = > \boxed{\theta = 90}$

Therefore

Angle between A and B will be 90°.