2021HSCShort answer

Q12 (e) (ii)

2 marks

Question

Using part (i), or otherwise, show that
$4\overrightarrow{GH}+\overrightarrow{GS}=\vec0.$

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Writes $\overrightarrow{GA}=\overrightarrow{GH}+\overrightarrow{HA}$ , or equivalent merit	1

Sample answer:

$\overrightarrow{GA}=\overrightarrow{GH}+\overrightarrow{HA}$
$\overrightarrow{GB}=\overrightarrow{GH}+\overrightarrow{HB}$
$\overrightarrow{GC}=\overrightarrow{GH}+\overrightarrow{HC}$
$\overrightarrow{GD}=\overrightarrow{GH}+\overrightarrow{HD}$

Adding these:

$\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD}=4\overrightarrow{GH}+\overrightarrow{HA}+\overrightarrow{HB}+\overrightarrow{HC}+\overrightarrow{HD}$
$-\overrightarrow{GS}=4\overrightarrow{GH}+\vec 0$
$\therefore4\overrightarrow{GH}+\overrightarrow{GS}=\vec0$

[Diagram present in source.]

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

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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