Assertion: If `theta` be the angle between `vec(A)` and `vec(B)`, then
`tan theta= (vec(A)xxvec(B))/(vec(A).vec(B))`
Reason: `vec(A)xxvec(B)` is perpendicualr to `vec(A).vec(B)`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false.
D. If both aseertion and reason are false.

Answer

D

Explanation

`(vec(A)xxvec(B))/(vec(A).vec(B))=(AB sin thetahat(n))/(AB cos theta)=tan theta`
where `hat(n)` is unit vector perpendicular to both `vec(A)` and `vec(B)`
However `(|vec(A)xxvec(B)|)/(vec(A).vec(B))= tan theta`