# What is the value of (A x B)^2 + (A * B)^2 ?

## Please interpret this as the sum of the squares of the cross product and dot product of two vectors A and B. Thanks:)

Nov 29, 2016

#### Answer:

${\left\mid A \right\mid}^{2} {\left\mid B \right\mid}^{2}$

#### Explanation:

$\left\mid A \times B \right\mid = \left\mid A \right\mid \left\mid B \right\mid \sin \phi$
$\left\mid A \cdot B \right\mid = \left\mid A \right\mid \left\mid B \right\mid \cos \phi$

here $\phi$ is the angle between $A$ and $B$ at common tails.

then

${\left\mid A \times B \right\mid}^{2} + {\left\mid A \cdot B \right\mid}^{2} = {\left\mid A \right\mid}^{2} {\left\mid B \right\mid}^{2} \left({\sin}^{2} \phi + {\cos}^{\phi}\right) = {\left\mid A \right\mid}^{2} {\left\mid B \right\mid}^{2}$