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Vectors and matrices — Question 11

QCAA 2022, Paper 1 · 6 marks

Q11 · 2022 · Technology-freeSimple familiar6 marks

QUESTION 11 (6 marks)

The position vector of a particle, r1\mathbf r_1 (cm), over time, tt (s), is given by r1(t)=(2t+1)i^+(t+3)j^−(2t−3)k^.\mathbf r_1(t)=(2t+1)\hat{\mathbf i}+(t+3)\hat{\mathbf j}-(2t-3)\hat{\mathbf k}.
a)
Determine the velocity vector of the particle.
[1 mark]
b)
Determine the time when the position vector of the particle is perpendicular to its velocity vector.
[2 marks]
c)
The position vector of a second particle is r2(t)=(16−4t)i^−(3t−13)j^+2k^\mathbf r_2(t)=(16-4t)\hat{\mathbf i}-(3t-13)\hat{\mathbf j}+2\hat{\mathbf k}. Determine whether the two particles collide.
[3 marks]
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