Question

Find the dot product of two vectors if their lengths are 2 and 1/9 and the angle between them is π/4. (give your answer correct to at least three decimal places.)

Answer 1

The formula of the dot product of two vectors:

$\overrightarrow{u}\circ\overrightarrow{v}=|\overrightarrow{u}|\cdot|\overrightarrow{v}|\cos\alpha$

We have:

$|\overrightarrow{u}|=2\\|\overrightarrow{v}|=\dfrac{1}{9}\\\alpha=\dfrac{\pi}{4}\to\cos\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}$

Substitute:

$\overrightarrow{u}\circ\overrightarrow{v}=9\cdot\dfrac{1}{9}\cdot\dfrac{\sqrt2}{2}=\dfrac{\sqrt2}{2}$