# Find a dot b given that ...(please see description)? Thanks

## Suppose $\vec{\text{OA}} = a$, $\vec{\text{OB}} = b$, $| a | = 3$, $| b | = \sqrt{7}$ and $a \times b = i + 2 j - 3 k$ Find $a \cdot b$

Jun 26, 2017

$\pm 7.$

#### Explanation:

We know that,

$| \vec{a} \cdot \vec{b} {|}^{2} + | \vec{a} \times \vec{b} {|}^{2} = | \vec{a} {|}^{2} | \vec{b} {|}^{2.}$

$\therefore | \vec{a} \cdot \vec{b} {|}^{2} + {\left\{\sqrt{{1}^{1} + {2}^{2} + {\left(- 3\right)}^{2}}\right\}}^{=} {3}^{2} {\left(\sqrt{7}\right)}^{2.}$

$\therefore | \vec{a} \cdot \vec{b} {|}^{2} + 14 = 63.$

$\therefore | \vec{a} \cdot \vec{b} {|}^{2} = 49.$

$\Rightarrow \vec{a} \cdot \vec{b} = \pm 7.$