2021HSCShort answer

Q12 (e) (iii)

1 mark

Question

Find the value of $\lambda$ such that $\overrightarrow{HG}=\lambda\overrightarrow{HS}$ .

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	1

Sample answer:

From part (ii):

$4\overrightarrow{GH}+\overrightarrow{GS}=\vec0$
$4\overrightarrow{GH}+\overrightarrow{GH}+\overrightarrow{HS}=\vec0$
$5\overrightarrow{GH}+\overrightarrow{HS}=\vec0$
$\overrightarrow{HS}=-5\overrightarrow{GH}=5\overrightarrow{HG}$
$\overrightarrow{HG}=\frac15\overrightarrow{HS}$
$\therefore\lambda=\frac15$

[Diagram present in source.]

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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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