Question 1313

Vectors II: Lines and Planes

2013 Paper 2 Question 4 Variant

Question

The planes

{p_1}

and

{p_2}

has equations

{\mathbf{r} \cdot \begin{pmatrix} - 4 \\ 1 \\ 8 \end{pmatrix} = 1}

and

{\mathbf{r} \cdot \begin{pmatrix} 6 \\ - 2 \\ 3 \end{pmatrix} = - 5}

respectively, and meet in the line

{l.}

(i)

Find the acute angle between

{p_1}

and

{p_2.}

[3]

(ii)

Find a vector equation for

{l.}

[4]

(iii)

The point

{A \left( 0, 4, c \right)}

is equidistant from

{p_1}

and

{p_2.}

Calculate the two possible values of

{c.}

[6]

Answer

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