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Vectors and matrices — Question 12

QCAA 2020, Paper 1 · 8 marks

Q12 · 2020 · Technology-freeSimple familiar8 marks

QUESTION 12 (8 marks)

Consider the vertices A, B and C of the rectangular prism as shown.
Rectangular prism showing vertices A, B and C and coordinate axes
a)
State the coordinates of A, B and C.
[1 mark]
b)
Determine a unit vector, n^\hat{\mathbf n}, that is normal to the plane containing A, B and C.
[3 marks]
c)
Verify that n^\hat{\mathbf n} is perpendicular to AB→\overrightarrow{AB}.
[2 marks]
d)
Determine the Cartesian equation of the plane containing A, B and C.
[2 marks]
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