2020HSCShort answer

Q15 (b) (ii)

1 mark

Question

Using the same definitions as in part (i), prove that
$\overrightarrow{OC}=\frac m{m+n}\mathbf a+\frac n{m+n}\mathbf b.$

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	1

Sample answer:

\overrightarrow{OC}=\overrightarrow{OA}+\overrightarrow{AC}

=\vec a+\frac n{m+n}(\vec b-\vec a)

=\vec a\left(1-\frac n{m+n}\right)+\frac n{m+n}\vec b

=\frac m{m+n}\vec a+\frac n{m+n}\vec b

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Syllabus alignment

Vectors

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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