# How do I find the dot product of <2, 3> and <4, −7>?

Oct 2, 2014

Let's begin by naming our vectors.

v$= < 2 , 3 >$
w$= < 4 , - 7 >$

Find the product of the horizontal components, $i$.
Find the product of the vertical components, $j$.
Then add those $2$ products together.

v$\cdot$w$= {v}_{i} \cdot {w}_{i} + {v}_{j} \cdot {w}_{j}$

v$\cdot$w$= \left(2\right) \left(4\right) + \left(3\right) \left(- 7\right)$

v$\cdot$w$= 8 - 21$

v$\cdot$w$= - 13$