# How do I find the dot product of vectors v =2i-3j and w= i-j?

Sep 5, 2014

The answer is $5$.

The dot product is the easier calculation to do with vectors. It is the sum of the product of the components:

$v \cdot w = {v}_{1} \cdot {w}_{1} + {v}_{2} \cdot {w}_{2}$
$= 2 \left(1\right) + \left(- 3\right) \left(- 1\right)$
$= 5$

The computation is the same regardless of the number of components in the vector, but the vectors must be the same size.

Recall that we can find the angle between the 2 vectors with the formula:

$v \cdot w = | | v | | \cdot | | w | | \cdot \cos \theta$