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

Find the value of $k$ such that the vectors $\begin{pmatrix} k \\ 2 \\ -1 \end{pmatrix}$ and $\begin{pmatrix} 3 \\ k \\ 5 \end{pmatrix}$ are perpendicular.

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

Determine the value of $k$ such that the vectors $\begin{pmatrix} 2k \\ k-1 \\ 3 \end{pmatrix}$ and $\begin{pmatrix} 4 \\ 2 \\ -6 \end{pmatrix}$ are perpendicular.

Determine the value of $k$ such that the vector $\begin{pmatrix} k \\ 3 \\ k-2 \end{pmatrix}$ is perpendicular to the vector $\begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix}$.

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

Find $k$ so that the vectors $\begin{pmatrix} k \\ 4 \\ 1 \end{pmatrix}$ and $\begin{pmatrix} 2 \\ 8 \\ 2 \end{pmatrix}$ are parallel.

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

Determine the value of $k$ such that the vectors $\begin{pmatrix} 3 \\ k \\ -9 \end{pmatrix}$ and $\begin{pmatrix} 6 \\ 4 \\ -18 \end{pmatrix}$ are parallel.

Find all $k \neq 0$ for which the vectors $\begin{pmatrix} 2k \\ 4k \\ -6k \end{pmatrix}$ and $\begin{pmatrix} 1 \\ 2 \\ -3 \end{pmatrix}$ are parallel.

Find the values of $k$ for which the vectors $\begin{pmatrix} 1 \\ k \\ 2 \end{pmatrix}$ and $\begin{pmatrix} 3 \\ 6 \\ k \end{pmatrix}$ are parallel.

Find the value(s) of $k$ such that the vectors $\begin{pmatrix} k^2 \\ k \\ 1 \end{pmatrix}$ and $\begin{pmatrix} 1 \\ -2 \\ 1 \end{pmatrix}$ are parallel.