Question

Find two unit vectors orthogonal to both
(8, 9, 1)
and
(−1, 1, 0)

Answer 1

when two vectors are othogonal, their dot product must be "0"

let the vector be \(\vec{u}=(a,b,c)\)

Answer 2

then
\[
{\rm 1:}\quad (8,9,1)\cdot(a,b,c)=0\\
8a+9b+c=0
\]
similarly, for the second one.
then it is given that \(\vec{u}\) is a unit vector. so, we get "3" equations in a, b, and c

Answer 3

\[\pm\frac{\vec u \times \vec v}{|\vec u \times \vec v|}\]