Question 1209

Vectors I: Basics, Dot and Cross Products

2009 Paper 2 Question 2 Variant

Question

Relative to the origin

{O,}

two points

{A}

and

{B}

have position vectors given by

{\mathbf{a}=- 13 \mathbf{i} + 3 \mathbf{j} + 22 \mathbf{k}}

and

{\mathbf{b}=23 \mathbf{i} + 39 \mathbf{j} + 6 \mathbf{k} }

respectively.

(i)

The point

{P}

divides the line

{AB}

in the ratio

{1:3.}

Find the coordinates of

{P.}

[2]

(ii)

Explain why

{AB}

and

{OP}

are perpendicular.

[2]

(iii)

The vector

{\mathbf{c}}

is a unit vector in the direction of

{\overrightarrow{OP}.}

Write

{\mathbf{c}}

as a column vector.

[1]

(iv)

Find the area of triangle

{OAP.}

[3]

Answer

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