Question

If $\vec{A} \times \vec{B}|=| \vec{A} \cdot \vec{B} \mid$ then the angle between $\vec{A}$ and $\vec{B}$ will be :

• A. $90^{\circ}$
• B. $60^{\circ}$
• C. $45^{\circ}$
• D. $30^{\circ}$

Answer 1

Answer: (C)

$45^{\circ}$

Answer 2

The modulii of cross and dot product of vector $\vec{A}$ and $\vec{B}$ are $A B \sin \theta$ and $A B \cos \theta$ respectively. Therefore, the given condition, $A B \sin \theta=A B \cos \theta$ or $\tan \theta=1$ or $\theta=45^{\circ}$