Question 1207

Vectors I: Basics, Dot and Cross Products

2007 Paper 1 Question 6 Variant

Question

Referred to the origin

{O,}

the position vectors of the points

{A}

and

{B}

are

\begin{align*} && 3 \mathbf{i} - 5 \mathbf{j} + 3 \mathbf{k} \\ \textrm{ and } \quad && \mathbf{i} + 3 \mathbf{j} + p \mathbf{k} \end{align*}

respectively.

(i)

Find the value of

{p.}

[2]

(ii)

Find the position vector of the point

{M}

on the line segment

{AB}

such that

{AM:MB = 2:3.}

[3]

(iii)

The point

{C}

has position vector

{5 \mathbf{i} - \mathbf{j} - 4 \mathbf{k}.}

Use a vector product to find the exact area of triangle

{OAC.}

[4]