2020HSCShort answer

Q15 (b) (iv)

1 mark

Question

Using parts (ii) and (iii), or otherwise, prove that $T$ is the point that divides the interval $PR$ in the ratio $2:1$ .

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	1

Sample answer:

By part (ii) the point which divides $PR$ in the ratio $2:1$ is given by

\frac23\vec r+\frac13\vec p,

but this is $\overrightarrow{OT}$ .

\therefore T\text{ divides the interval }PR\text{ in the ratio }2:1.

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Syllabus alignment

Working MathematicallyVectors

Introduction to three-dimensional vectorsRepresent and operate with vectors in three dimensions using unit, component, ordered-triple and column-vector forms.

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