RevisionDojo

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

Question 1

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

[4]

Question 2

The question requires using the condition for perpendicular vectors, where the scalar (dot) product is equal to zero, to find the value of an unknown constant.

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

[3]

Question 3

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

[5]

Question 4

The vectors $\mathbf{a}$ and $\mathbf{b}$ are parallel if and only if there exists a non-zero scalar $\lambda$ such that $\mathbf{a} = \lambda\mathbf{b}$ .

Determine the value(s) of $k$ for which the vectors $\begin{pmatrix} 1 \\ k \\ 2 \\ \end{pmatrix}$ and $\begin{pmatrix} k \\ -1 \\ 3 \\ \end{pmatrix}$ are parallel.

[4]

Question 5

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

[4]

Question 6

For what value(s) of $k$ are the vectors $\begin{pmatrix} k \\ 2k \\ 3 \end{pmatrix}$ and $\begin{pmatrix} 1 \\ -4 \\ 1 \end{pmatrix}$ perpendicular?

[3]

Question 7

Topic 3: Geometry and trigonometry — 3.12 Vector product, perpendicular vectors.

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

[4]

Question 8

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

[3]

Question 9

For what value(s) of $k$ are the vectors $\begin{pmatrix} 1 \\ k \\ 2 \end{pmatrix}$ and $\begin{pmatrix} k \\ -1 \\ 3 \end{pmatrix}$ perpendicular?

[4]

Question 10

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

[4]

Question 11

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

[3]

Question 12

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

[4]

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