Question 1312

Vectors II: Lines and Planes

2012 Paper 1 Question 9 Variant

Question

(i)

Find a vector equation of the line through the points

{A}

and

{B}

with position vectors

{- 7 \mathbf{i} + 3 \mathbf{j} + 9 \mathbf{k}}

and

{- 13 \mathbf{i} + 3 \mathbf{j} + 9 \mathbf{k}}

respectively.

[3]

(ii)

The perpendicular to this line from the point

{C}

with position vector

{- 9 \mathbf{i} + 6 \mathbf{j} + 12 \mathbf{k}}

meets the line at the point

{N.}

Find the position vector of

{N}

and the ratio

{AN:NB.}

[5]

(iii)

Find the cartesian equation of the line which is a reflection of the line

{AC}

in the line

{AB.}

[4]