IB Mathematics Analysis and Approaches Question Type 5: Finding for What Value of a Parameter Are 2 Vectors Parallel or Perpendicular Exercises

For what $k$ are the vectors $\left(\begin{array}{c}{k}^2\\ k\\ 1\end{array}\right)$ and $\left(\begin{array}{c}1\\ -2\\ 1\end{array}\right)$ perpendicular?

Find the value of $k$ such that the vectors $\left(\begin{array}{c}k\\ 2\\ -1\end{array}\right)$ and $\left(\begin{array}{c}3\\ k\\ 5\end{array}\right)$ 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 $\left(\begin{array}{c}2k\\ k-1\\ 3\end{array}\right)$ and $\left(\begin{array}{c}4\\ 2\\ -6\end{array}\right)$ are perpendicular.

Determine the value of $k$ such that the vector $\left(\begin{array}{c}k\\ 3\\ k-2\end{array}\right)$ is perpendicular to the vector $\left(\begin{array}{c}1\\ -1\\ 2\end{array}\right)$.

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

Find $k$ so that the vectors $\left(\begin{array}{c}k\\ 4\\ 1\end{array}\right)$ and $\left(\begin{array}{c}2\\ 8\\ 2\end{array}\right)$ 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 $\left(\begin{array}{c}3\\ k\\ -9\end{array}\right)$ and $\left(\begin{array}{c}6\\ 4\\ -18\end{array}\right)$ are parallel.

Find all $k\ne 0$ for which the vectors $\left(\begin{array}{c}2k\\ 4k\\ -6k\end{array}\right)$ and $\left(\begin{array}{c}1\\ 2\\ -3\end{array}\right)$ are parallel.

Find the values of $k$ for which the vectors $\left(\begin{array}{c}1\\ k\\ 2\end{array}\right)$ and $\left(\begin{array}{c}3\\ 6\\ k\end{array}\right)$ are parallel.

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