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Vectors and matrices — Question 11

QCAA 2024, Paper 1 · 4 marks

Q11 · 2024 · Technology-freeSimple familiar4 marks

QUESTION 11 (4 marks)

The vector equation of a straight line is given by (xy)=(20)+k(−12),\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}2\\0\end{pmatrix}+k\begin{pmatrix}-1\\2\end{pmatrix}, where kk is a scalar.
a)
Express the equation of the line as a pair of parametric equations.
[1 mark]
b)
Use your result from Question 11a) to express the equation of the line as a Cartesian equation.
[1 mark]
c)
Determine the coordinates of the point that the line passes through when k=5k=5.
[1 mark]
d)
Determine the value of kk when the line intersects the yy-axis.
[1 mark]
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