JEE Main & Advanced Physics Vectors Question Bank Topic Test - Vectors

\[\vec{A}-\vec{B}\] and \[\vec{A}\] are parallel. If \[|\vec{A}\times \vec{B}|\,=\,|\vec{A}.\vec{B}|,\] then angle between \[\vec{A}\] and \[\vec{B}\] will be

A) \[30{}^\circ \]

B) \[45{}^\circ \]

C) \[60{}^\circ \]

D) \[90{}^\circ \]

Correct Answer: B

Solution :

[b] \[\left| \overrightarrow{A}\times \overrightarrow{B} \right|=\overrightarrow{A}.\overrightarrow{B}\]

\[\Rightarrow \] \[\,AB\sin \theta \,=\text{ }AB\text{ }\cos \theta \]

\[\Rightarrow \] \[\tan \,\theta =1\]

\[\therefore \] \[\theta \text{ }=\text{ }{{45}^{o}}\]