Question

The sum and difference of two vector equal in magnitude i.e. | ⃗⃗⃗⃗A + ⃗⃗⃗⃗B | = | ⃗⃗⃗⃗A – ⃗⃗⃗⃗B |. What will  be the angle b/w ⃗⃗⃗⃗A & ⃗⃗⃗⃗B

pls give correct answers its urgent​

Answer 1

Given:

• The sum and difference of two vector equal in magnitude i.e,

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

To find:

• Angle between A and B .

Solution:

$\implies \: | \vec{A} + \vec{B}| = | \vec{A} - \vec{B}| \\ \\ \implies \: \cancel{A}^{2} + \cancel {B ^{2} } + 2AB \cos \theta = \cancel A {}^{2} + \cancel{B {}^{2}} - 2AB \cos \theta \: \\ \\ \implies \: 4AB \cos \theta = 0 \\ \\ \implies \: \cos \theta = 0 \\ \\ \implies \: \theta = 90 \degree$

Hence, the angle between A and B is 90°