If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vector, the angle between these Vector is

Options

A. ` 0^@`
B. (b) ` 90^@`
C. (45^@`
D. ` 180^@`

Answer

B

Explanation

Give , `| vec A+vec B| =| vec A-vec B|`
or ` sqrt(A^2 +B^2 + 2 B cos theta)`
` = sqrt A^2 +B^2 = 2 AB cos theta)` ltbRgt or ` A^2 + B^2 + 2 AB cos theta = A^2 + B^2 - 2 AB cos theta`
or ` 4 AB cos theta = 0 ` or ` cos theta = 0` or `theta = 90^@`.