Edexcel A-Level Mathematics A2 P4.7.4 Position Vectors Questions

Practise Edexcel IAL P4.7.4 position vectors by subtracting OB and OA, finding missing coordinates, and relating collinear points.

Exam points

Calculate AB by subtracting position vectors in i, j, k or column form
Find a missing point by adding a displacement vector to a known position vector
Use position-vector ratios to relate collinear points

[Maximum number: 3]

Relative to a fixed origin O, the points A, B and C have position vector a, b and c respectively.

Points A, B and C lie in a straight line, with B lying between A and C.
Given A B: A C=1: 3 show that

\mathbf{c}=3 \mathbf{b}-2 \mathbf{a}

M1: Attempts any two of $\overrightarrow{A B}, \overrightarrow{A C}$ and $\overrightarrow{B C}$ .
Condone the wrong way around but it must be subtraction.
Allow marked in the correct place on a diagram
dM1: Uses the given information.
Accept $\overrightarrow{A B}=\frac{1}{3} \overrightarrow{A C}, \quad \overrightarrow{B C}=2 \times \overrightarrow{A B}, \quad \overrightarrow{B C}=\frac{2}{3} \times \overrightarrow{A C} \quad$ etc condoning slips as in previous M1.
A1*: Fully correct work inc bracketing leading to the given answer c=3 b-2 a
Expect to see the brackets multiplied out. So $\mathbf{c}-\mathbf{b}=2 \times(\mathbf{b}-\mathbf{a}) \Rightarrow \mathbf{c}-\mathbf{b}=2 \mathbf{b}-2 \mathbf{a} \Rightarrow \mathbf{c}=3 \mathbf{b}-2 \mathbf{a}$ is fine.

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Edexcel A-Level Mathematics A2 P4.7.4 Position Vectors Questions question 1