Statement I : If $θ be the angle between \vec{A} and \vec{B}, then tanθ = \frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}}$
Statement II : $\vec{A} \times \vec{B} is perpendicular to \vec{A} . \vec{B}$

Moderate

A

If both statement I and statement II are true and statement II is the correct explanation of statement I.
B

If both statement I and statement II are true but statement II is not the correct explanation of statement I.
C

If statement I is true but statement II is false.
D

If both statement I and statement II are false.

Solution

$\frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}} = \frac{ABsinθ \hat{n}}{ABcosθ} = tanθ \hat{n}$
where $\hat{n} is unit vector perpendicular to both \vec{A} and \vec{B} .$
However $\frac{| \vec{A} \times \vec{B} |}{\vec{A} . \vec{B}} = tanθ$

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