IB Mathematics Applications & Interpretation Question Type 4: Finding for What Values of a Parameter Are Two Vectors Perpendicular Exercises

For what value(s) of $k$ are the vectors $\left(\frac{1}{k},k,2\right)$ and $(3,1,k)$ perpendicular?

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

Determine the value(s) of $k$ for which the vectors $\left(\begin{array}{c}\frac{1}{k}\\ k\\ 2\end{array}\right)$ and $\left(\begin{array}{c}3\\ 1\\ k\end{array}\right)$ are parallel.

Determine the value(s) of $k$ for which the vectors $\left(\begin{array}{c}1\\ k\\ 2\end{array}\right)$ and $\left(\begin{array}{c}k\\ -1\\ 3\end{array}\right)$ are 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 $\left(\begin{array}{c}k\\ 2k\\ 3\end{array}\right)$ and $\left(\begin{array}{c}1\\ -4\\ 1\end{array}\right)$ perpendicular?

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 $(k,2k,3)$ and $(1,-4,1)$ parallel?

For what value(s) of $k$ are the vectors $\left(\begin{array}{c}1\\ k\\ 2\end{array}\right)$ and $\left(\begin{array}{c}k\\ -1\\ 3\end{array}\right)$ 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 $(k,k^2,1)$ and $(2,1,-1)$ perpendicular?

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