# 1987 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 1987 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

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##### 1987 A Level H2 Math Paper 1 Question 18 [Modified]

The points $A$, $B$, $C$, $D$ have position vectors $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$, $\mathbf{d}$ given by $\mathbf{a}=\mathbf{i}+2\mathbf{j}+3\mathbf{k}$, $\mathbf{b}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}$, $\mathbf{c}=3\mathbf{i}+2\mathbf{j}+\mathbf{k}$, $\mathbf{d}=4\mathbf{i}-\mathbf{j}-\mathbf{k}$, respectively. The point $P$ lies on $AB$ produced such that $AP=2AB$, and the point $Q$ is the midpoint of $AC$.

(i)

Show that $PQ$ is perpendicular to $AQ$.

[4]

(i) Show that $PQ$ is perpendicular to $AQ$.

[4]

(ii)

Find the area of the triangle $APQ$.

[2]

(ii) Find the area of the triangle $APQ$.

[2]

(iii)

Find a vector perpendicular to the plane $ABC$.

[3]

(iii) Find a vector perpendicular to the plane $ABC$.

[3]

(iv)

Find the cosine of the angle between $\overrightarrow{AD}$ and $\overrightarrow{BD}$.

[3]

(iv) The point $D$ lies on the line $CN$ produced and is such that $N$ is the mid-point of $CD$.
Find the position vector of $D$.

[2]

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