IB Mathematics Applications & Interpretation Topic AHL 3.13—scalar and Vector Products Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 3.13—scalar and Vector Products Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.13—scalar and Vector Products with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.13—scalar and Vector Products and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

A survey drone releases a sensor pod. Its position vector relative to a fixed origin $O$ , at time $t$ seconds ( $t \geq 0$ ), is described by $r (t) = 6 + 5 t 9 - 3 t 12 + 7 t - 3 t^{2}$ , where the $z$ -axis is vertical and all distances are in metres.

Demonstrate that the sensor pod moves in a vertical plane and specify an equation of this plane.

[4]

Determine a vector expression for the velocity of the sensor pod at time $t$ .

[2]

By calculating the scalar product, verify that the velocity of the sensor pod is orthogonal to the normal vector $3 i + 5 j$ of this plane at all times.

[2]

Find a vector expression for the acceleration of the sensor pod at time $t$ .

[3]

Calculate the time when the sensor pod passes the point $(21, 0, 6)$ .

[3]

Determine the speed of the sensor pod as it passes this point.

[3]

Question 2

HLPaper 1

Determine the value of $k$ such that $u$ and $v$ are collinear.

[2]

Determine the value of $k$ such that $u$ and $v$ are orthogonal.

[4]

Question 3

HLPaper 1

Consider the vector $P Q = 123$ .

Calculate the magnitude $∣ P Q ∣$ .

[2]

Given the vector $P R = 3 - 1 2$ , determine the size of the angle $Q \hat{P} R$ .

[4]

Question 4

HLPaper 1

Determine a simplified algebraic expression for the dot product $u \cdot v$ in terms of $k$ .

[2]

Determine the range of values for $k$ such that the angle between $u$ and $v$ is obtuse.

[4]

Question 5

HLPaper 1

Consider the vector $U V = 112$ .

Calculate the magnitude $∣ U V ∣$ .

[2]

Given the vector $U W = 202$ , determine the size of the angle $V \hat{U} W$ .

[4]

IB Mathematics Applications & Interpretation AHL 3.13—scalar and Vector Products Questionbank

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IB Mathematics Applications & Interpretation AHL 3.13—scalar and Vector Products Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 3.13—scalar and Vector Products Questionbank

Unlock all 45 questions with a free account