Question

Can anyone take a look at the vector problem below?

Answer 1

`|vec a|=3`

Explanation:

The dot product of two vectors `vec a` and `vec b` is given by `|vec a| |vec b| cos(theta)`, where `theta` is the angle between them.

Since `vec a*vec b=18` and `|vec b|=4|vec a|`, `18=|vec a| |vec b| cos(60^@)=1/2|vec a| |vec b|=2|vec a|^2`. Rearrange this to get `|vec a|^2=9`, or `|vec a|=3`.