Question 1307

Vectors II: Lines and Planes
2007 Paper 1 Question 8 Variant

Question

The line l{l} passes through the points A{A} and B{B} with coordinates (0,3,1){\left( 0, - 3, 1 \right)} and (2,2,1){\left( 2, 2, 1 \right)} respectively. The plane p{p} has equation x+3y4z=52.{- x + 3 y - 4 z = - 52.} Find
(i)
The coordinates of the point of intersection of l{l} and p,{p,}
[5]
(ii)
The acute angle between l{l} and p,{p,}
[3]
(iii)
The perpendicular distance from A{A} to p.{p.}
[3]

Answer