Question 1313

Vectors II: Lines and Planes
2013 Paper 2 Question 4 Variant

Question

The planes p1{p_1} and p2{p_2} has equations r(841)=0{\mathbf{r} \cdot \begin{pmatrix} - 8 \\ 4 \\ - 1 \end{pmatrix} = 0} and r(430)=2{\mathbf{r} \cdot \begin{pmatrix} - 4 \\ 3 \\ 0 \end{pmatrix} = - 2} respectively, and meet in the line l.{l.}
(i)
Find the acute angle between p1{p_1} and p2.{p_2.}
[3]
(ii)
Find a vector equation for l.{l.}
[4]
(iii)
The point A(4,4,c){A \left( -4, -4, c \right)} is equidistant from p1{p_1} and p2.{p_2.} Calculate the two possible values of c.{c.}
[6]

Answer