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IB Maths AI HL Ahl 3 10 Hl Vectors Questions

Practise representing and combining directed segments with vectors, calculating magnitudes and unit vectors, and interpreting the result in geometric or applied contexts.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Represent directed segments with vectors and use scalar multiplication, base vectors, components and column notation.
  • Add, subtract and normalise vectors, calculate magnitudes and unit vectors, and determine resultants.
  • Interpret vector algebra in a geometric or applied context, checking direction, scale and units.

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Study AHL 3.10 (HL)—Vectors conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Ahl 3 10 Hl Vectors Questions question 1

[Maximum number: 4]

In this question, all distances are in kilometres and t is in hours.
Let (100)\left(\begin{smallmatrix}1\\0\\0\end{smallmatrix}\right) be a displacement of 1 km due east, (010)\left(\begin{smallmatrix}0\\1\\0\end{smallmatrix}\right) be a displacement of 1 km due north, and (001)\left(\begin{smallmatrix}0\\0\\1\end{smallmatrix}\right) be a vertical displacement of 1 km.
Highway 85 in Saudi Arabia is a long, straight, flat road.
Relative to the centre of the town Arar, point O, the position vector of a car, C, travelling along this road is given by:

OC→=(10−50)+t(50−330)\overrightarrow{\mathrm{OC}}=\left(\begin{array}{c}10\\-5\\0\end{array}\right)+t\left(\begin{array}{c}50\\-33\\0\end{array}\right)

The police are testing a long-range drone, D, to monitor cars travelling along this road. The drone is launched at t=0 from the point with position vector (200−1000.02)\left(\begin{smallmatrix}200\\-100\\0.02\end{smallmatrix}\right) and flies in a straight line with a constant height of 0.02 km and a constant velocity of (−15−200)\left(\begin{smallmatrix}-15\\-20\\0\end{smallmatrix}\right).

Question (a)

(a)

Find the speed of the car.

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Question (b)

(b)

Find an expression for CD→\overrightarrow{\mathrm{CD}}, the relative position of the drone from the car.

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