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AHL 3.13—Scalar and vector products - IB Questionbank | RevisionDojo

Practice AHL 3.13—Scalar and vector products with authentic IB Mathematics Applications & Interpretation (AI) 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 IB examiners.

Paper

Level

Question 1

HLPaper 1

Let $=\left[\begin{array}{c}2 \\ -1 \\ 1\end{array}\right]$ and $=\left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right]$ .

Find the area of the triangle formed by vectors and .

[4]

Question 2

HLPaper 2

Let $=\left[\begin{array}{c}2 \\ -2 \\ 1\end{array}\right]$ and $=\left[\begin{array}{l}0 \\ 1 \\ 3\end{array}\right]$ .

Show that the angle between the vectors is acute.

[4]

Question 3

HLPaper 1

Let $=\left[\begin{array}{c}2 \\ -2 \\ 1\end{array}\right]$ .

Find a unit vector in the same direction as .

[2]

Question 4

HLPaper 1

Let $=\left[\begin{array}{c}1 \\ 3 \\ -2\end{array}\right]$ and $=\left[\begin{array}{c}4 \\ -1 \\ x\end{array}\right]$ .

Find the value of x such that the angle between and is $90^{\circ}$ .

[4]

Question 5

HLPaper 1

Let $=\left[\begin{array}{c}2 \\ -3 \\ 1\end{array}\right],=\left[\begin{array}{c}-1 \\ 4 \\ 2\end{array}\right]$ , and $=\left[\begin{array}{c}3 \\ -2 \\ 5\end{array}\right]$ .

Determine whether the three vectors lie in the same plane.

[4]

Question 6

HLPaper 1

Let $=\left[\begin{array}{c}1 \\ 2 \\ -1\end{array}\right],=\left[\begin{array}{c}x \\ 2 x \\ -x\end{array}\right]$ .

Find the value of x such that $\cdot \vec{b}=6$ .

[2]

Question 7

HLPaper 1

Let $=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$ , and let $x$ represent the magnitude.

Find $x$ .

[2]

Question 8

HLPaper 1

Show that the vectors $=\left[\begin{array}{c}1 \\ 2 \\ -1\end{array}\right]$ and $=\left[\begin{array}{c}2 \\ 4 \\ -2\end{array}\right]$ are parallel.

[3]

Question 9

HLPaper 2

Let $=\left[\begin{array}{c}x \\ 1 \\ -2\end{array}\right]$ and $=\left[\begin{array}{c}3 \\ -2 \\ 4\end{array}\right]$ .

Given that $\cdot \vec{b}=0$ , find the value of $x$ .Hence, determine the angle between $\vec{a}$ and $\vec{b}$ .

[3]

Question 10

HLPaper 2

Let $=\left[\begin{array}{c}2 \\ -1 \\ 3\end{array}\right]$ and $=\left[\begin{array}{c}-1 \\ 4 \\ 0\end{array}\right]$ .

Find the angle $\theta$ between the two vectors, in degrees.

[6]

AHL 3.13—Scalar and vector products Questionbank