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Vector operations - MYP Questionbank | RevisionDojo

Practice Vector operations 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

Solve the following vector equation for $x$ and $y$ :

\begin{pmatrix} x \\ y \end{pmatrix} + 2 \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}

Question 2

Calculate the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \pi \\ 1 \end{pmatrix}$ , giving the answer correct to three significant figures.

Question 3

If $|\mathbf{a}| = 5$ , $|\mathbf{b}| = 4$ , and the angle between the two vectors is $60^\circ$ , calculate the dot product $\mathbf{a} \cdot \mathbf{b}$ .

Question 4

Determine the value of the scalar $k$ such that the vector $\mathbf{u} = \begin{pmatrix} k \\ 6 \end{pmatrix}$ is parallel to the vector $\mathbf{v} = \begin{pmatrix} k-2 \\ 2 \end{pmatrix}$ .

Question 5

Which of the following vectors is parallel to $\mathbf{v} = \begin{pmatrix} 1.2 \\ 3.0 \end{pmatrix}$ and contains the smallest possible positive integer components?

Question 6

Consider the following statement:

"The dot product of the zero vector $\mathbf{0} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$ and any vector $\mathbf{v} = \begin{pmatrix} x \\ y \end{pmatrix}$ is always the scalar 0."

Which of the following is correct?

Question 7

True or False: If the dot product of two vectors $\mathbf{a}$ and $\mathbf{b}$ is zero ( $\mathbf{a} \cdot \mathbf{b} = 0$ ), it must be true that the vectors are perpendicular.

Question 8

Solve the vector equation for all possible values of $x$ :

\begin{pmatrix} x^2 - 10 \\ 5 \end{pmatrix} = \begin{pmatrix} 6 \\ x - 1 \end{pmatrix}

Question 9

The vectors $\mathbf{u} = \binom{4}{10}$ and $\mathbf{v} = \binom{x}{x+3}$ are parallel. Determine the value of $x$ .

Question 10

Which of the following vectors is in the same direction as $\mathbf{w} = \begin{pmatrix} 0.5 \\ -0.75 \end{pmatrix}$ and has the smallest possible integer components?

Type

Difficulty

Question 1

Solve the following vector equation for $x$ and $y$ :

\begin{pmatrix} x \\ y \end{pmatrix} + 2 \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}

Question 2

Calculate the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \pi \\ 1 \end{pmatrix}$ , giving the answer correct to three significant figures.

Question 3

If $|\mathbf{a}| = 5$ , $|\mathbf{b}| = 4$ , and the angle between the two vectors is $60^\circ$ , calculate the dot product $\mathbf{a} \cdot \mathbf{b}$ .

Question 4

Determine the value of the scalar $k$ such that the vector $\mathbf{u} = \begin{pmatrix} k \\ 6 \end{pmatrix}$ is parallel to the vector $\mathbf{v} = \begin{pmatrix} k-2 \\ 2 \end{pmatrix}$ .

Question 5

Which of the following vectors is parallel to $\mathbf{v} = \begin{pmatrix} 1.2 \\ 3.0 \end{pmatrix}$ and contains the smallest possible positive integer components?

Question 6

Consider the following statement:

"The dot product of the zero vector $\mathbf{0} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$ and any vector $\mathbf{v} = \begin{pmatrix} x \\ y \end{pmatrix}$ is always the scalar 0."

Which of the following is correct?

Question 7

True or False: If the dot product of two vectors $\mathbf{a}$ and $\mathbf{b}$ is zero ( $\mathbf{a} \cdot \mathbf{b} = 0$ ), it must be true that the vectors are perpendicular.

Question 8

Solve the vector equation for all possible values of $x$ :

\begin{pmatrix} x^2 - 10 \\ 5 \end{pmatrix} = \begin{pmatrix} 6 \\ x - 1 \end{pmatrix}

Question 9

The vectors $\mathbf{u} = \binom{4}{10}$ and $\mathbf{v} = \binom{x}{x+3}$ are parallel. Determine the value of $x$ .

Question 10

Which of the following vectors is in the same direction as $\mathbf{w} = \begin{pmatrix} 0.5 \\ -0.75 \end{pmatrix}$ and has the smallest possible integer components?

Type

Difficulty

Question 1

Solve the following vector equation for $x$ and $y$ :

\begin{pmatrix} x \\ y \end{pmatrix} + 2 \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ 4 \end{pmatrix}

Question 2

Calculate the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \pi \\ 1 \end{pmatrix}$ , giving the answer correct to three significant figures.

Question 3

If $|\mathbf{a}| = 5$ , $|\mathbf{b}| = 4$ , and the angle between the two vectors is $60^\circ$ , calculate the dot product $\mathbf{a} \cdot \mathbf{b}$ .

Question 4

Determine the value of the scalar $k$ such that the vector $\mathbf{u} = \begin{pmatrix} k \\ 6 \end{pmatrix}$ is parallel to the vector $\mathbf{v} = \begin{pmatrix} k-2 \\ 2 \end{pmatrix}$ .

Question 5

Which of the following vectors is parallel to $\mathbf{v} = \begin{pmatrix} 1.2 \\ 3.0 \end{pmatrix}$ and contains the smallest possible positive integer components?

Question 6

Consider the following statement:

"The dot product of the zero vector $\mathbf{0} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$ and any vector $\mathbf{v} = \begin{pmatrix} x \\ y \end{pmatrix}$ is always the scalar 0."

Which of the following is correct?

Question 7

True or False: If the dot product of two vectors $\mathbf{a}$ and $\mathbf{b}$ is zero ( $\mathbf{a} \cdot \mathbf{b} = 0$ ), it must be true that the vectors are perpendicular.

Question 8

Solve the vector equation for all possible values of $x$ :

\begin{pmatrix} x^2 - 10 \\ 5 \end{pmatrix} = \begin{pmatrix} 6 \\ x - 1 \end{pmatrix}

Question 9

The vectors $\mathbf{u} = \binom{4}{10}$ and $\mathbf{v} = \binom{x}{x+3}$ are parallel. Determine the value of $x$ .

Question 10

Which of the following vectors is in the same direction as $\mathbf{w} = \begin{pmatrix} 0.5 \\ -0.75 \end{pmatrix}$ and has the smallest possible integer components?

Vector operations Questionbank