If `|vecA+vecB|=|vecA|+|vecB|`, then angle between `vecA` and `vecB` will be

Options

A. `90^(@)`
B. `120^(@)`
C. `0^(@)`
D. `60^(@)`

Answer

C

Explanation

(c): `|vecA+vecB|=|vecA|+|vecB|`
Let `|vecA+vecB|^(2)|=|vecA^(2)+|vecB|^(2)+2vecA.vecB`
`|vecA+vecB|^(2)|=|vecA^(2)|+|vecB|^(2)+2vecA.vecB`
From equation
`(|vecA|+|vecB|)^(2)=|vecA|^(2)+|vecB|^(2)+2|vecA||vecB|cos theta`
`rArr |vecA|^(2)+|vecB|^(2)+2|vecA||vecB|=|vecA|^(2)+2|vecA||vecB| cos theta`
`rArr cos theta =1`
`rArr theta=0^(@)`