# How do you compute the dot product for u=3i+4j and v=7i-2j?

Jun 23, 2016

13

#### Explanation:

If $u = \left({a}_{1} i + {b}_{1} j\right) = \left({a}_{1} , {b}_{1}\right) \mathmr{and} v = \left({a}_{2} i + {b}_{2} j\right) = \left({a}_{2} , {b}_{2}\right)$,

then the dot (scalar) product

$u . v = \left({a}_{1} , {b}_{1}\right) . \left({a}_{2} , {b}_{2}\right) = {a}_{1} {b}_{1} + {a}_{2} {b}_{2}$.

Here, $u . v = \left(3 , 4\right) . \left(7 , - 2\right) = \left(3\right) \left(7\right) + \left(4\right) \left(- 2\right) = 21 - 8 = 13$.