Question

I have this question:

u = (1,2,2) v=(1,0,7)

Determine all vectors of length 1 that are orthogonal to both the u and v¨

Answer 1

Let \((x,y,z)\) be a vector that is orthogonal to both the vectors \(u\) and \(v\)

Answer 2

What do you know about the relation between `dot product` and `orhogonal vectors` ?

Answer 3

isn't that if we use the dot product and our result is 0 then the vectors are orthogonal? @ganeshie8

Answer 4

yeah, or we could also use the cross product.... depends on what the OP knows...

Answer 5

\[U \times V = \left[\begin{matrix}1 & 2 & 2 \\ 1 & 0 & 7\end{matrix}\right] = (14,-5,-2)\]

\[\pm \frac{ U \times V }{ \left| U \times V \right| } = \pm \frac{ 1 }{ 15 }(13,-5,-2)\]

Answer 6

Looks perfect!