It is found that `|A+B|=|A|`,This necessarily implies.

Options

A. B=0
B. A, B are antiparallel
C. A, B are perpendicular
D. `A.B le 0`

Answer

A, B

Explanation

Given that `" " |A+B|=|A| or |A+B|^(2)=|A|^(2)`
`rArr " " |A|^(2)+|B|^(2)+2|A||B|cos theta=|A|^(2)`
where `theta` is angle between A and B.
`rArr " " |B|(|B|+2|A|cos theta)=0`
`rArr " " |B|=0 or |B|+2|A|cos theta=0`
`rArr " " cos theta =-(|B|)/(2|A|)`
If A and B are antiparallel, then `theta=180^(@)`
Hence , from Eq. (i)
`-1=-(|B|)/(2|A|)rArr |B|=2|A|`
Hence, correct answer will be either |B|=0 or B are antiparallel provided |B|=2|A|