Question

`vec(A)` and `vec(B)` are two Vectors and `theta` is the angle between them, if `|vec(A)xxvec(B)|= sqrt(3)(vec(A).vec(B))` the value of `theta` is
A. `60^(@)`
B. `45^(@)`
C. `30^(@)`
D. `90^(@)`

Answer 1

Correct Answer - A
`vec(A)xxvec(B)= AB sin theta` and `vec(A).vec(B)= AB cos theta`
Given, `|vec(A)xxvec(B)|=sqrt(3)(vec(A).vec(B))`
`implies AB sin theta= sqrt(3) AB cos theta`
`implies tan theta= sqrt(3)`
`theta= 60^(@)`