How many QCAA Specialist Mathematics Alternative Sequence questions cover Algebra of vectors in two dimensions?

AusGrader has 8 QCAA Specialist Mathematics Alternative Sequence questions on Algebra of vectors in two dimensions, all with instant AI grading and detailed marking feedback.

QCAA Specialist Mathematics Alternative Sequence Algebra of vectors in two dimensions

1 sample question with marking guides and sample answers

2021

QCAA

Paper 1

1 mark

Car A moves with a velocity of $v_A=2\hat{\mathbf{i}}-5\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

Car B moves with a velocity of $v_B=3\hat{\mathbf{i}}+6\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

The velocity of Car A relative to Car B is

$-\hat{\mathbf{i}}-11\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

$-\hat{\mathbf{i}}+\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

$\hat{\mathbf{i}}+11\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

$5\hat{\mathbf{i}}+\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

Reveal Answer

$-\hat{\mathbf{i}}-11\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

Correct Answer

The relative velocity of Car A with respect to Car B is found by subtracting B's velocity from A's: $v_{A/B} = v_A - v_B = (2-3)\hat{\mathbf{i}} + (-5-6)\hat{\mathbf{j}} = -\hat{\mathbf{i}} - 11\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$ .

$-\hat{\mathbf{i}}+\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

This incorrect answer results from a sign error when subtracting the $\hat{\mathbf{j}}$ components, calculating $-5 - (-6)$ instead of $-5 - 6$ .

$\hat{\mathbf{i}}+11\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

This is the velocity of Car B relative to Car A ( $v_B - v_A$ ), which is the exact opposite of the requested relative velocity.

$5\hat{\mathbf{i}}+\hat{\mathbf{j}}\ \mathrm{m\ s^{-1}}$

This is the sum of the two velocities ( $v_A + v_B$ ), rather than the difference required to find relative velocity.

QCAA Specialist Mathematics Alternative Sequence Algebra of vectors in two dimensions

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