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Two vectors vec(A) and vec( B) are drawn...

Two vectors `vec(A)` and `vec( B)` are drawn from a common point and `vec(C)=vec(A)+vec(B)`

A

If `C^(2)=A^(2)+B^(2)` , the angle between vectors `vec(A)` and `vec(B)` is `90^(@)`

B

If `C^(2)lt A^(2)+B^(2)` , the angle between `vec(A)` and `vec(B)` is greater than `90^(@)`

C

If `C^(2)gt A^(2)+B^(2)` , then angle between the `vec(A)` and `vec(B)` is between`0^(@)` and `90^(@)`

D

If `C=A-B` , angle between the vectors `vec(A)` and `vec(B)` is `180^(@)` .

Text Solution

Verified by Experts

The correct Answer is:
D
`C^(2)=A^(2)+B^(2)+2AB cos theta`
`If theta=90^(@)`
then `C^(2)=A^(2)+B^(2)`
if `theta gt 90^(@)`
then `C^(2)=A^(2)+B^(2)+2ABcos theta lt A^(2)+B^(2)` ltBRgt `:. cos theta` will be negative
If `theta lt 90^(@)`
then `C^(2)=A^(2)+B^(2)+2ABcos theta gtA^(2)+B^(2)`
If `:. C=A-B rArrtheta=180^(@)`
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