Study Pure Mathematics notes on Vector Equations for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the A-Level Pure Mathematics notes from September 2020. It is a free notes for revision.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 43
Monday 14 September 2020
ANSWERS
20 MARKS
NB: If a numerical answer cannot be given exactly, and the accuracy required is not specified in the question, then in the case of an angle it should be given to the nearest degree, and in other cases it should be given correct to $\mathbf{2}$ significant figures.
1. Find the vector equation of the line of intersection of the planes $x-2 y+z=2$ and
\[
2 x-y+3 z=6
\]
[5]
Let $z=t$
(i)
\[
\begin{array}{l}
x-2 y+t=2
\Rightarrow x=2+2 y-t
\end{array}
\]
\[
\begin{array}{l}
2 x-y+3 z=6
\Rightarrow 2(2+2 y-t)-y+3 t=6
\Rightarrow 4+4 y-2 t-y+3 t=6
\Rightarrow 3 y=6-4-t
\Rightarrow 3 y=2-t
\Rightarrow y=\frac{2}{3}-\frac{1}{3} t
\end{array}
\]
Now:
\[
\begin{array}{l}
x=2+2 y-t
\Rightarrow x=2+2\left(\frac{2}{3}-\frac{1}{3} t\right)-t
\Rightarrow x=2+\frac{4}{3}-\frac{2}{3} t-t
\end{array}
\]
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