IB Maths AA HL Ahl 3 12 Hl Vectors Questions

Practise constructing, combining and interpreting vectors in component or i,j,k form, including magnitudes, geometry, motion and multi-step spatial models.

Exam points

Construct position, displacement and directed-segment vectors from points, diagrams or vector relations, including component and i,j,k forms.
Add, subtract and scale vectors, express unknown vectors in terms of given vectors, and use components or collinearity to determine parameters and coordinates.
Calculate vector magnitudes, distances, speeds and unit vectors, and interpret the result in a geometric or physical context.
Use vector algebra to prove geometric facts such as parallel sides, parallelograms, collinearity, midpoint relations or equal lengths.
Apply vector representations to motion and spatial models, evaluating positions, separations, rates or optimisation quantities at specified times.

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Study AHL 3.12 (HL)—Vectors conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 3]

Consider the points A(1,2,3), B(k,-2,1) and C(5,0,2), where $k \in \mathbb{R}$ .

(a)

Write down $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{AC}}$ .

[ 2 ]

$\quad \overrightarrow{\mathrm{AB}}=\left(\begin{array}{c}k-1 \\ -4 \\ -2\end{array}\right), \overrightarrow{\mathrm{AC}}=\left(\begin{array}{c}4 \\ -2 \\ -1\end{array}\right)$

(b)

Given that the points A, B and C lie on a straight line, show that k=9.

[ 1 ]

METHOD 1
$k-1=2 \times 4$ M1
k=9
METHOD 2
in order by y or z-ordinate, the points are (k,-2,1),(5,0,2)(1,2,3)
k-5=5-1
k=9
AG

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IB Maths AA HL Ahl 3 12 Hl Vectors Questions question 1

Question (a)

Question (b)