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 (1,1,3){\left( 1, 1, - 3 \right)} and (2,1,1){\left( 2, - 1, - 1 \right)} respectively. The plane p{p} has equation 5x+2y+3z=23.{5 x + 2 y + 3 z = - 23.} 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