Study Pure Mathematics revision pack on Planes and Lines from Trockers. Useful for tertiary revision, coursework support, and exam preparation in Zimbabwe.
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This is the A-Level Pure Mathematics revision pack from September 2020. It is a free revision pack for revision.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 35
Tuesday 01 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 equation of the plane which contains the lines $L_{1}: \boldsymbol{r}=\left(\begin{array}{c}-1 2 3\end{array}\right)+s\left(\begin{array}{c}1 -3 2\end{array}\right)$ and
\[
L_{2}: \boldsymbol{r}=\left(\begin{array}{c}
2
0
-1
\end{array}\right)+s\left(\begin{array}{c}
-5
15
-10
\end{array}\right) .
\]
[4]
\[
\begin{array}{l}
d_{1}=\left(\begin{array}{c}
1
-3
2
\end{array}\right)
d_{2}=\left(\begin{array}{c}
-5
15
-10
\end{array}\right)=-5\left(\begin{array}{c}
1
-3
2
\end{array}\right)=-5 d_{1}
\end{array}
\]
$\therefore d_{1}$ and $d_{1}$ are parallel
The two lines are of the form $\boldsymbol{L}_{\mathbf{1}}: \boldsymbol{r}=\boldsymbol{a}_{\mathbf{1}}+t \boldsymbol{d}_{\mathbf{1}}$ and $\boldsymbol{L}_{\mathbf{2}}: \boldsymbol{r}=\boldsymbol{a}_{\mathbf{2}}+t \boldsymbol{d}_{\mathbf{2}}$
A river cuts through a rock not because of its power, but its persistence.
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