# What is the dot product of <5,-3,6 > and <-8,2,-9 >?

Jan 6, 2017

$- 100$

#### Explanation:

the dot product of two vectors

veca=((a_1),(a_2),(a_3)), &vecb=((b_1),(b_2),(b_3)),

can be calculated by the result

$\vec{a} . \vec{b} = {a}_{1} {b}_{1} + {a}_{2} {b}_{2} + {a}_{3} {b}_{3}$

in this case we have

veca=((5),(-3),(6)), &vecb=((-8),(2),(-9)),

$\vec{a} . \vec{b} = 5 \times \left(- 8\right) + \left(- 3\right) \times 2 + 6 \times \left(- 9\right)$

$\vec{a} . \vec{b} = - 40 - 6 - 54 = - 100$