RevisionDojo

Vector representation - MYP Questionbank | RevisionDojo

Practice Vector representation with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

In a parallelogram $ABCD$ , the position vectors of three vertices relative to an origin $O$ are $\overrightarrow{OA} = \mathbf{a}$ , $\overrightarrow{OB} = \mathbf{b}$ , and $\overrightarrow{OC} = \mathbf{c}$ . Find the position vector of the fourth vertex, $\overrightarrow{OD}$ .

Question 2

Given the vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ , find the vector $\mathbf{a} + 2\mathbf{b}$ .

Question 3

Let $\mathbf{a}$ and $\mathbf{b}$ be non-zero and non-parallel vectors. Which of the following statements about the vectors $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ is always true?

Question 4

In a quadrilateral $PQRS$ , the vectors representing three sides are $\overrightarrow{PQ} = \mathbf{a}$ , $\overrightarrow{QR} = \mathbf{b}$ , and $\overrightarrow{PS} = 2\mathbf{b}$ . Determine the vector $\overrightarrow{SR}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ .

Question 5

A drone moves from a starting point $O$ with an initial translation $\mathbf{d}_1 = 4\mathbf{i} - 3\mathbf{j}$ and then follows with a second translation $\mathbf{d}_2 = -2\mathbf{i} + 5\mathbf{j}$ . What is the total displacement from the start?

Question 6

Point $K$ lies on the line segment $LM$ produced (extended) such that $\overrightarrow{LK} = 1.5 \overrightarrow{LM}$ . If $\overrightarrow{OL} = \mathbf{l}$ and $\overrightarrow{OM} = \mathbf{m}$ , express $\overrightarrow{MK}$ in terms of $\mathbf{l}$ and $\mathbf{m}$ .

Question 7

Fill in the blank: The vector expression $3(2\mathbf{i} - \mathbf{j}) + 4\mathbf{j}$ can be simplified and written as the column vector ________.

Question 8

True or False: If the position vectors of points $P$ and $Q$ are $\mathbf{p}$ and $\mathbf{q}$ respectively, then the displacement vector $\overrightarrow{PQ}$ is calculated as $\mathbf{p} - \mathbf{q}$ .

Question 9

Let $\mathbf{u}$ and $\mathbf{v}$ be non-zero vectors such that $\mathbf{u} = k\mathbf{v}$ for some non-zero scalar $k$ . Which of the following statements about their directions is always correct?

Question 10

Which of the following expressions correctly represents the vector journey $\overrightarrow{DC}$ by going through point $B$ ?

Type

Difficulty

Question 1

Question 2

Given the vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ , find the vector $\mathbf{a} + 2\mathbf{b}$ .

Question 3

Let $\mathbf{a}$ and $\mathbf{b}$ be non-zero and non-parallel vectors. Which of the following statements about the vectors $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ is always true?

Question 4

Question 5

Question 6

Question 7

Fill in the blank: The vector expression $3(2\mathbf{i} - \mathbf{j}) + 4\mathbf{j}$ can be simplified and written as the column vector ________.

Question 8

Question 9

Let $\mathbf{u}$ and $\mathbf{v}$ be non-zero vectors such that $\mathbf{u} = k\mathbf{v}$ for some non-zero scalar $k$ . Which of the following statements about their directions is always correct?

Question 10

Which of the following expressions correctly represents the vector journey $\overrightarrow{DC}$ by going through point $B$ ?

Type

Difficulty

Question 1

Question 2

Given the vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ , find the vector $\mathbf{a} + 2\mathbf{b}$ .

Question 3

Let $\mathbf{a}$ and $\mathbf{b}$ be non-zero and non-parallel vectors. Which of the following statements about the vectors $\mathbf{a} + \mathbf{b}$ and $\mathbf{a} - \mathbf{b}$ is always true?

Question 4

Question 5

Question 6

Question 7

Fill in the blank: The vector expression $3(2\mathbf{i} - \mathbf{j}) + 4\mathbf{j}$ can be simplified and written as the column vector ________.

Question 8

Question 9

Let $\mathbf{u}$ and $\mathbf{v}$ be non-zero vectors such that $\mathbf{u} = k\mathbf{v}$ for some non-zero scalar $k$ . Which of the following statements about their directions is always correct?

Question 10

Which of the following expressions correctly represents the vector journey $\overrightarrow{DC}$ by going through point $B$ ?

Vector representation Questionbank