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

Represent points and displacements with position vectors and i, j, k components, then calculate magnitudes, unit vectors, sums and scalar multiples.
Use vector algebra to prove geometric properties such as parallelism, collinearity, ratios or perpendicular relationships, showing the required component or dot-product steps.

[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)