Let the angle between two non - zero vectors `vec(A)` and `vec(B)` be `120^(@)`and its resultant be `vec( C)`.

Options

A. `|vec(C)|` must be equal to `|vec(A)- vec(B)|`
B. `|vec(C)|` must be less than `|vec(A)- vec(B)|`
C. `|vec(C)|` must be greater than `|vec(A)- vec(B)|`
D. `|vec(C)|` may be equal to `|vec(A)- vec(B)|`

Answer

B

Explanation

`theta= 120^(@)`
`|vec(C)|= |vec(R)|`
`rArr sqrt(A^(2) + B^(2) + 2AB cos theta)= sqrt(A^(2) + B^(2) + 2AB (- (1)/(2)))`
`= sqrt(A^(2) + B^(2)- AB)`
Now, `|vec(A)- vec(B)|= sqrt(A^(2) + B^(2) + 2AB cos (180- theta))`
`= sqrt(A^(2) + B^(2) + 2AB cos (180- theta))`
`= sqrt(A^(2)+ B^(2) + 2AB cos 60^(@))= sqrt(A^(2) + B^(2) + AB)`
`therefore |vec(C)| lt |vec(A)- vec(B)|`