Question 1311

Vectors II: Lines and Planes

2011 Paper 1 Question 11 Variant

Question

The plane

{p}

passes through the points with coordinates

{\left( - 1, - 2, 0 \right),}

{\left( - 3, 4, - 5 \right)}

{\left( 0, 4, - 2 \right).}

(i)

Find a cartesian equation of

{p.}

[4]

The line

{l_1}

has equation

\frac{x + 6}{2} = \frac{y + 8}{2} = z + 2

and the line

{l_2}

has equation

\frac{x + 18}{- 3} = \frac{y + 4}{5} = \frac{z + 13}{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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