How do you find the sum of the unit vectors (-1,2,-4) and (-8,5,-10)?

Nov 15, 2016

The unit vector is: $\left(- \frac{9}{\sqrt{326}} , \frac{7}{\sqrt{326}} , - \frac{14}{\sqrt{326}}\right)$

Explanation:

The sum is:

$\left(- 1 , 2 , - 4\right) + \left(- 8 , 5 , - 10\right) = \left(- 9 , 7 , - 14\right)$

To make a unit vector, compute the magnitude:

|(-9. 7, -14)| = sqrt((-9)^2 + 7^2 + (-14)^2) = sqrt(326)

Divide each component by $\sqrt{326}$

The unit vector is: $\left(- \frac{9}{\sqrt{326}} , \frac{7}{\sqrt{326}} , - \frac{14}{\sqrt{326}}\right)$