1 Answer | Add Yours
Two vectors are orthogonal if their scalar product is equal to 0. So let's first find vector `y=<<y_1,y_2,y_3>>` which is orthogonal to `u` and `v`. To do that we will solve the following system of equations:
We have two equations with three unknowns, hence infinitely many solutions. Let's choose the solution with `y_1=1`.
`8+2y_2-5y_3=0 ` (1)
(1)-(2)= `18+5y_2=0 => y_2=-18/5`
`8+2(-18/5)-5y_3=0 => y_3=4/25`
Hence `y=<<1,-18/5,4/25>>`. To get unit vector `x` we need to devide `y` by its length `||y||=sqrt(y_1^2+y_2^2+y_3^2)`
We’ve answered 319,622 questions. We can answer yours, too.Ask a question