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vec(A) and vec(B) are two Vectors and th...

`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^(@)`

Text Solution

Verified by Experts

The correct Answer is:
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^(@)`
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