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Vectors and matrices — Question 9

QCAA 2020, Paper 2 · 1 mark

Q9 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 9

Two objects, P and Q, move in three-dimensional space such that their positions, r\mathbf r, over time, tt, are described by the following vectors until they collide.
rP=(t2−4t)i^+(2t2−t+3)j^−(6−5t)k^\mathbf r_P=(t^2-4t)\hat{\mathbf i}+(2t^2-t+3)\hat{\mathbf j}-(6-5t)\hat{\mathbf k}
rQ=(−t2+2t)i^+(3t+t2)j^+t2k^\mathbf r_Q=(-t^2+2t)\hat{\mathbf i}+(3t+t^2)\hat{\mathbf j}+t^2\hat{\mathbf k}
The objects will collide at
(A)
t=0t=0
(B)
t=1t=1
(C)
t=2t=2
(D)
t=3t=3
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