Question

Find a vector that has the opposite direction of u = (1,-2,4), but which has length square root of 3.

Answer 1

Normalize
`\vec u` by dividing
`\vec u` by its magnitude:

`(\vec u)/(\|\vec u\|)=((1,-2,4))/(√(1^2+(-2)^2+4^2))=((1,-2,4))/(√(21))`

Multiply by -1 to reverse its direction, and again by
`\sqrt3` to ensure this new vector has the magnitude we want. Notice that
`\sqrt{\frac3{21}}=\frac1{\sqrt7}`.

`-\sqrt3(\vec u)/(\|\vec u\|)=((-1,2,-4))/(\sqrt7)`