IB Mathematics Analysis and Approaches Topic AHL 3.16—vector Product Questionbank (HL)

IB Mathematics Analysis and Approaches Topic AHL 3.16—vector Product Questionbank (HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 3.16—vector Product with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.16—vector Product and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 1

Consider points $A (1, - 3, 4)$ , $B (3, - 2, 6)$ , $C (2, - 1, 2)$ .

Find $A B$ and $A C$ .

[3]

Compute angle $B A C$ . Give your answer in degrees or radians.

[4]

Find the unit vector in the direction $A C - A B$ .

[3]

Find the distance from $A$ to the line $B C$ .

[3]

Question 2

HLPaper 1

The coordinates of the points $P, Q, R$ and $S$ are $(4, 1, - 1)$ , $(3, 3, 5)$ , $(1, 0, 2 c)$ and $(1, 1, 2)$ respectively. The vectors $QR$ and $P R$ are orthogonal.

Find the value of $c$ .

[6]

Hence, calculate $P S \times P R$ .

[4]

Hence, find the vector equation of the line $l$ which passes through the point $Q$ and is parallel to the vector $P R$ .

[3]

Question 3

HLPaper 2

The diagram below shows the parallelepiped $A B C D E F G H$ . The position vectors of $A, C, D$ and $E$ are $a c d e = i + 4 j - k = i + j + 7 k = 2 i - j + k = - 4 i + 2 j + 3 k$ in that order. The point $X$ lies on the line segment $[E C]$ and satisfies $E X = λ E C$ .

Find the least possible value of $∣ H X ∣$ , giving your answer exactly and to $3$ significant figures.

[14]

Question 4

HLPaper 1

Line $L_{1}$ : $r = 123 + λ 4 - 1 2$ and plane $π$ : $2 x - y + z = 5$ .

Find the point of intersection of the line $L_{1}$ and the plane $π$ .

[4]

Determine if the line $L_{1}$ is parallel, perpendicular, or neither to the normal of the plane $π$ .

[4]

Question 5

HLPaper 1

Let $u = 2 i - j + 3 k$ and $v = i + 4 j - 2 k$ .

Find $u \times v$ .

[3]

Hence find a unit vector that is perpendicular to both $u$ and $v$ .

[2]

IB Mathematics Analysis and Approaches AHL 3.16—vector Product Questionbank

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IB Mathematics Analysis and Approaches AHL 3.16—vector Product Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 3.16—vector Product Questionbank

Unlock all 15 questions with a free account