Question

v = 4i - 2j + k
Find a vector orthogonal to both v and i + j.

Answer 1

u have two vectors \(v=4i-2j+k=(4,-2,1)\) and \(w=i+j=(1,1,0)\).

u r looking for a vector \(u=xi+yj+zk=(x,y,z)\) such that
\[ \large \begin{cases}
0=v\cdot u=4x-2y+z\\ 0=w\cdot u=x+y
\end{cases} \]