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Vectors and matrices — Question 12

QCAA 2021, Paper 1 · 8 marks

Q12 · 2021 · Technology-freeSimple familiar8 marks

QUESTION 12 (8 marks)

Consider the plane x−y−2z=15x-y-2z=15.
a)
Determine a vector n\mathbf n that is perpendicular to the plane.
[1 mark]
b)
Determine the vector equation of the line ll that is perpendicular to the plane and contains the point A(−2,1,3)(-2,1,3).
[1 mark]
c)
Use the result from Question 12b) to express the equation of the line ll in parametric form.
[1 mark]
d)
The line ll and the plane intersect at point S. Show that the coordinates of S are (2,−3,−5)(2,-3,-5).
[3 marks]
e)
Determine AS→\overrightarrow{AS}.
[1 mark]
f)
Use a property of parallel vectors to verify that AS→\overrightarrow{AS} and n\mathbf n are parallel.
[1 mark]
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