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Question 35

Relative to a fixed origin $O$ :

the point $A$ has position vector $1i+2j−k1\mathbf{i} + 2\mathbf{j} - \mathbf{k}$
the point $B$ has position vector $3i−2j+7k3\mathbf{i} - 2\mathbf{j} + 7\mathbf{k}$

The line $l$ passes through $A$ and $B$ .

(i) Find $AB→\overrightarrow{AB}$ . (ii) Find a vector equation for the line $l$ .

[3]

The point $C$ has position vector $9i+0j+1k9\mathbf{i} + 0\mathbf{j} + 1\mathbf{k}$ . The point $P$ lies on $l$ . Given that $CP→\overrightarrow{CP}$ is perpendicular to $l$ :

Find the position vector of the point $P$ .

[5]

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