Question

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

Answer 1

`r = 9.64` `"units"`

Explanation:

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

`< color(red)(-6), color(blue)(1), color(green)(-3)> - < color(red)(4), color(blue)(6), color(green)(5)> = < color(red)(2), color(blue)(-5), color(green)(-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"`