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(418)=3{\mathbf{r} \cdot \begin{pmatrix} - 4 \\ - 1 \\ - 8 \end{pmatrix} = - 3} and r(263)=5{\mathbf{r} \cdot \begin{pmatrix} 2 \\ - 6 \\ 3 \end{pmatrix} = - 5} 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(1,1,c){A \left( -1, 1, c \right)} is equidistant from p1{p_1} and p2.{p_2.} Calculate the two possible values of c.{c.}
[6]

Answer