Question

If $\mathbf{|}\overrightarrow{\mathbf{A}}\mathbf{\times }\overrightarrow{\mathbf{B}}\mathbf{|}\mathbf{=}\overrightarrow{\mathbf{A}}\mathbf{·}\overrightarrow{\mathbf{B}}$what is the angle between$\overrightarrow{\mathbf{A}}\mathit{a}\mathit{n}\mathit{d}\overrightarrow{\mathbf{B}}$ ?

Short answer

The required angle is $45.0°$

Step-by-step solution

Given Data

$|\overline{A}\times \overline{B}|=\overline{A}·\overline{B}$

Concept

A and B both are the vector quantity. The multiplication of vectors has two methods one is dot and another is cross. Both are expressed in the below step.

Find the angle between the  

On applying the dot and cross method of multiplication of the vectors we will get

$\begin{array}{c}|\overrightarrow{A}\times \overrightarrow{B}|=\overrightarrow{A}·\overrightarrow{B}\\ \text{AB\hspace{0.17em}sin\hspace{0.17em}}\theta =\text{AB\hspace{0.17em}}\cos \theta \\ \text{tan\hspace{0.17em}}\theta =1\\ \theta =45.0°\end{array}$

So the required angle is $45.0°$