# What is || <-6, 1, -3 > - < 4 , 6, 5 > ||?

Jul 2, 2017

$r = 9.64$ $\text{units}$

#### Explanation:

Subtracting two vectors with known components like these is straightforward: you simply subtract each of the components to get your resultant vector:

$< \textcolor{red}{- 6} , \textcolor{b l u e}{1} , \textcolor{g r e e n}{- 3} > - < \textcolor{red}{4} , \textcolor{b l u e}{6} , \textcolor{g r e e n}{5} > = < \textcolor{red}{2} , \textcolor{b l u e}{- 5} , \textcolor{g r e e n}{- 8} >$

The magnitude of this resultant vector is given by the three-dimensional distance formula:

r = sqrt((2)^2 + (-5)^2 + (-8)^2) = color(purple)(9.64 color(purple)("units"