Question Type 4: Finding for what values of a parameter are two vectors perpendicular Exercises

For what value(s) of $k$ are the vectors $(k^2,k,1)$ and $(1,-2,1)$ perpendicular?

For what value(s) of $k$ are the vectors $(1,k,2)$ and $(k,-1,3)$ perpendicular?

For what value(s) of $k$ are the vectors $(k,2k,3)$ and $(1,-4,1)$ perpendicular?

For what value(s) of $k$ are the vectors $(2,k,3)$ and $(k,4,-1)$ perpendicular?

For what value(s) of $k$ are the vectors $(k,k^2,1)$ and $(2,1,-1)$ perpendicular?

For what value(s) of $k$ are the vectors $(k^2,k,1)$ and $(1,-2,1)$ parallel?

For what value(s) of $k$ are the vectors $(\tfrac1k,k,2)$ and $(3,1,k)$ perpendicular?

For what value(s) of $k$ are the vectors $(k,2k,3)$ and $(1,-4,1)$ parallel?

For what value(s) of $k$ are the vectors $(1,k,2)$ and $(k,-1,3)$ parallel?

For what value(s) of $k$ are the vectors $(2,k,3)$ and $(k,4,-1)$ parallel?

For what value(s) of $k$ are the vectors $(k,k^2,1)$ and $(2,1,-1)$ parallel?

For what value(s) of $k$ are the vectors $(\tfrac1k,k,2)$ and $(3,1,k)$ parallel?