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Specialist Maths — Question 15

QCAA 2020, Paper 1 · 6 marks

Q15 · 2020 · Technology-freeSimple familiar6 marks

QUESTION 15 (6 marks)

The points O (0,0,0)(0,0,0), A (−6,2,−2)(-6,2,-2) and C (3,1,2)(3,1,2) are represented in three-dimensional space in the diagram.
OABC forms a parallelogram in three-dimensional space.
Three-dimensional parallelogram OABC with points M and N
a)
Determine the coordinates of B.
[1 mark]
b)
M is the midpoint of BC. Determine the vector that represents OM→\overrightarrow{OM}.
[1 mark]
c)
N divides AM in the ratio 2:1. Determine the vector that represents ON→\overrightarrow{ON}.
[2 marks]
d)
Use a vector method to show that O, B and N lie on a straight line.
[2 marks]
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