Question

What is `|| <4, 5, -7 > - < 9, -2, 1 > ||`?

Answer 1

`|< 4,5,-7 > - < 9,-2,1 >|=sqrt(138)`

Explanation:

Given `veca=< 4,5,-7 >` and `vecb=< 9,-2,1 >`, we can subtract `vecb` from `veca` by subtracting the components of `vecb` from those of `veca`.

`< 4,5,-7 > - < 9,-2,1 >`

`=> < (4-9), (5-(-2)), (-7-1) >`

`=>< -5, 7, -8 >`

Let's call this new vector `vecc`, where `vecc=< c_x,c_y,c_z >`. The magnitude of `vecc` is then given by:

`|vecc|=sqrt((c_x)^2+(c_y)^2+(c_z)^2)`

`=>|vecc|=sqrt((-5)^2+(7)^2+(-8)^2)`

`=>|vecc|=sqrt(25+49+64)`

`=>|vecc|=sqrt(138)`

`:.|< 4,5,-7 > - < 9,-2,1 >|=sqrt(138)`