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}|=(1)/(9)\\\alpha=(\pi)/(4)\to\cos(\pi)/(4)=(\sqrt2)/(2)`

Substitute:

`\overrightarrow{u}\circ\overrightarrow{v}=9\cdot(1)/(9)\cdot(\sqrt2)/(2)=(\sqrt2)/(2)`