Question

if the magnitude of sum and difference of two vectors is the same the angle between them

Answer 1

$\bold{Hello}$

According to the question , the magnitude of sum and diffrence of two vectors is same.



Let the vectors be A and B and the angle between them $\bold{\theta}$ .



Magnitude of sum :-

$\bold{\sqrt{A^2 + B^2 + 2AB cos \theta}}$




Magnitude of diffrence :-

$\bold{\sqrt{A^2 + B^2 - 2AB cos \theta}}$



equate them and then
squaring both the sides.

We will get :-



→ 2AB cosθ = - 2AB cosθ

→ 4AB cosθ = 0

→ cosθ = 0

So , θ = 90°







Hope It Helps You. ^_^

Answer 2

Explanation:

According to the question , the magnitude of sum and diffrence of two vectors is same.

Let the vectors be A and B and the angle between them θ.

Magnitude of sum :-

$\sqrt{A^{2} + B^{2} + 2ABcos \theta}$

Magnitude of diffrence :-

$\sqrt{A^{2} + B^{2} - 2ABcos \theta}$

equate them and then

squaring both the sides.

We will get :-

→ 2AB cosθ = - 2AB cosθ

→ 4AB cosθ = 0

→ cosθ = 0

So , θ = 90°