For tow vectros ` vec A` and `vec B`
` | vec A + vec B| = | vec A- vec B|` is always true when.

Options

A. `|A|=|B|!= 0`
B. `A_|_B`
C. `|A|=|B|!= 0` and A and B are parallel or anti-parallel
D. when either |A| or |B| is zero

Answer

B, D

Explanation

Given, |A+B|=|A-B|
`rArr " " sqrt(|A|^(2)+|B|^(2)+2|A||B| cos theta)=sqrt(|A|^(2)+|B|^(2)-2|A||B|cos theta)`
`rArr " " |A|^(2)+|B|^(2)+2|A||B|cos theta = |A|^(2)+|B|^(2)-2|A||B|cos theta`
`rArr " " 4|A||B| cos theta =0`
`rArr " " |A||B|cos theta=0`
`rArr " " |A|=0 or |B| = 0 or cos theta =0`
`rArr " " theta=90^(@)`
When `theta=90^(@)`, we can say that `A_|_B`