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

Options

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

Answer

B, D

Explanation

(d): Since `|vecA+vecB|=|vecA|`
`|vecA+vecB|^(2)=|vecA|^(2)`
`vecA.vecA+vecA.vecB+vecB.vecA+vecB.vecB=|vecA|^(2)`
`rArr |vecA|^(2)+2vecA.vecB+|vecB|^(2)=|vecA|^(2)`
`rArr 2vecA.vecB+vecB.vecB=0`
`rArr vecB(2vecA+vecB)=0`
So, sither `vecB=0` or `2vecA+vecB=0` or `vecB= - 2vecA`
Options (a) and (b) may or may not be true .
`2vecA.vecB+|vecB|^(2)=0`
`rArr vecA.vecB le0`
The correct option is (d) .