Question

Find a unit vector in the direction of u and opposite of u

Answer 1

Just divide
`\mathbf u` by its magnitude:

`\|\mathbf u\|=√(5^2+6^2+(-1)^2)=√(62)`

So a unit vector in the direction of
`\mathbf u` is

`(\mathbf u)/(\|\mathbf u\|)=\frac5{√(62)}\,\mathbf i+\frac6{√(62)}\,\mathbf j-\frac1{√(62)}\,\mathbf k`

Then multiply this by -1 to get a unit vector pointing in the opposite direction.