Question 1310

Vectors II: Lines and Planes

2010 Paper 1 Question 10 Variant

Question

The line

{l}

has equation

\frac{x - 10}{2} = \frac{y - 4}{2} = \frac{z - 9}{-6},

and the plane

{p}

has equation

x + y - 3 z = 31.

(i)

Show that

{l}

is perpendicular to

{p.}

[2]

(ii)

Find the coordinates of the point of intersection of

{l}

and

{p.}

[4]

(iii)

Show that the point

{A}

with coordinates

{\left( 12, 6, 3 \right)}

lies on

{l.}

Find the coordinates of the point

{B}

which is the mirror image of

{A}

{p.}

[3]

(iv)

Find the area of triangle

{OAB,}

where

{O}

is the origin, giving your answer to the nearest whole number.

[3]