Question Type 5: Finding for what value of a parameter are 2 vectors parallel or perpendicular Bootcamps

Find all $k\neq0$ for which the vectors $(2k,4k,-6k)$ and $(1,2,-3)$ are parallel.

Find the value of $k$ such that the vectors $(k,2,-1)$ and $(3,k,5)$ are perpendicular.

Find $k$ so that the vectors $(k,4,1)$ and $(2,8,2)$ are parallel.

For which $k$ are the vectors $(2,k,4)$ and $(5,-1,1)$ perpendicular?

Determine $k$ such that the vectors $(2k,k-1,3)$ and $(4,2,-6)$ are perpendicular.

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

Determine $k$ such that $(k,3,k-2)$ is perpendicular to $(1,-1,2)$.

Determine $k$ so that the vectors $(3,k,-9)$ and $(6,4,-18)$ are parallel.

Find all values of $k$ for which the vectors $(k,2,-1)$ and $(3,k,5)$ are parallel.

Find all real $k$ such that $(k,k^2,1)$ is perpendicular to $(1,2,1)$.

Find the values of $k$ for which the vectors $(1,k,2)$ and $(3,6,k)$ are parallel.

Find $k$ so that the vectors $(k^2,k,1)$ and $(1,-2,1)$ are parallel.