Question 1315

Vectors II: Lines and Planes

2015 Paper 2 Question 2 Variant

Question

The line

{L}

has equation

\mathbf{r} = \left( 3 \mathbf{i} + 4 \mathbf{j} - 5 \mathbf{k} \right) + \lambda \left( 2 \mathbf{i} - 2 \mathbf{j} + \mathbf{k} \right).

(i)

Find the acute angle between

{L}

and the

{x}

-axis.

[2]

The point

{P}

has position vector

{- 2 \mathbf{i} + 5 \mathbf{k}.}

(ii)

Find the points on

{L}

which are a distance of

{\sqrt{134}}

from

{P.}

Hence or otherwise find the point on

{L}

which is closest to

{P.}

[5]

(iii)

Find a cartesian equation of the plane that includes the line

{L}

and the point

{P.}

[3]