Question 1311

Vectors II: Lines and Planes

2011 Paper 1 Question 11 Variant

Question

The plane

{p}

passes through the points with coordinates

{\left( 3, 7, - 3 \right),}

{\left( 1, - 1, 5 \right)}

{\left( - 5, - 5, - 1 \right).}

(i)

Find a cartesian equation of

{p.}

[4]

The line

{l_1}

has equation

\frac{x - 8}{2} = \frac{y - 7}{2} = z - 7

and the line

{l_2}

has equation

\frac{x - 10}{6} = \frac{y - 22}{- 7} = \frac{z - 9}{k},

where

{k}

is a constant. It is given that

{l_1}

and

{l_2}

intersect.

(ii)

Find the value of

{k.}

[4]

(iii)

Show that

{l_1}

lies in

{p}

and find the coordinates of the point at which

{l_2}

intersects

{p.}

[4]

(iv)

Find the acute angle between

{l_2}

and

{p.}

[3]

Answer

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