# If A= <2 ,7 ,-4 > and B= <-1, -4, 2 >, what is A*B -||A|| ||B||?

Nov 8, 2017

$\approx - - 76.066$ ( 3 .d.p.)

#### Explanation:

$A = \left(\begin{matrix}2 \\ 7 \\ - 4\end{matrix}\right)$

$B = \left(\begin{matrix}- 1 \\ - 4 \\ 2\end{matrix}\right)$

$A \cdot B = \left(\begin{matrix}- 2 \\ - 28 \\ - 8\end{matrix}\right) = \left(- 2\right) + \left(- 28\right) + \left(- 8\right) = - 38$

$| | A | | = \sqrt{{\left(2\right)}^{2} + {\left(7\right)}^{2} + {\left(- 4\right)}^{2}} = \sqrt{69}$

$| | B | | = \sqrt{{\left(- 1\right)}^{2} + {\left(- 4\right)}^{2} + {\left(2\right)}^{2}} = \sqrt{21}$

( we do not need to be concerned with negative roots, since the magnitude is an absolute value )

So we have:

$- 38 - \sqrt{69} \times \sqrt{21}$

= $- 38 - 3 \sqrt{23 \times 7}$

= $- 38 - 3 \sqrt{161}$

= $- 38 - 38.06573$

= $- 76.066$ ( 3 .d.p.)