Question 1212

Vectors I: Basics, Dot and Cross Products

2012 Paper 1 Question 5 Variant

Question

Referred to the origin

{O,}

the points

{A}

and

{B}

have position vectors

{\mathbf{a}}

and

{\mathbf{b}}

such that

\begin{align*} \mathbf{a} &= - 2 \mathbf{i} + 2 \mathbf{j} - \mathbf{k} \\ \textrm{and} \quad \mathbf{b} &= 2 \mathbf{i} + \mathbf{j} - \mathbf{k}. \end{align*}

The point

{C}

has position vector

{\mathbf{c}}

given by

{\mathbf{c}=\lambda \mathbf{a}+\mu \mathbf{b},}

where

{\lambda}

and

{\mu}

are positive constants.

(i)

Given that the area of triangle

{OAC}

is

{3 \sqrt{53},}

find

{\mu.}

[4]

(ii)

Given instead that

{\mu = 2}

and that

{OC = \sqrt{29},}

find the possible coordinates of

{C.}

[4]

Answer

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