Assertion: If `|vec(A)+vec(B)|=|vec(A)-vec(B)|`, then angle between `vec(A)` and `vec(B)` is `90^(@)`
Reason: `vec(A)+vec(B)= vec(B)+vec(A)`

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false.
D. If both aseertion and reason are false.

Answer

B

Explanation

`|vec(A)+vec(B)|=|vec(A)-vec(B)|`
`implies A^(2)+B^(2)+2AB cos theta= A^(2)+B^(2)+2AB cos theta`
Hence `cos theta` which gives `theta= 90^(@)`
Also vector addition is commulative.
Hence `vec(A)+vec(B)= vec(B)+vec(A)`.