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 (3,3,2){\left( 3, 3, 2 \right)} and (1,1,4){\left( 1, 1, 4 \right)} respectively. The plane p{p} has equation 5x+4yz=65.{5 x + 4 y - z = 65.} 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