Question

Question #03e79

Answer 1

`(1,1,3)` is an example of a vector orthogonal to `(1,2,-1)`.

Explanation:

If two vectors are orthogonal, then their dot product is 0. In this case we can pick two of the components and solve for the third, so I'll pick `(1,1,z)`. Taking the dot product:

`(1,1,z).(1,2,-1)=1*1+1*2+z(-1)=3-z`

Since we know the dot product should be zero, we have:

`3-z=0 \rightarrow z= 3`

So a non-zero vector orthogonal to `(1,2,-1)` is the vector `(1,1,3).`

You have two degrees of freedom in this problem, so if you pick two values and solve for the third it will keep working.