Question 1310

Vectors II: Lines and Planes
2010 Paper 1 Question 10 Variant

Question

The line l{l} has equation
x72=y3=z5,\frac{x - 7}{-2} = \frac{y}{3} = z - 5,
and the plane p{p} has equation
2x+3y+z=33.- 2 x + 3 y + z = 33.
(i)
Show that l{l} is perpendicular to p.{p.}
[2]
(ii)
Find the coordinates of the point of intersection of l{l} and p.{p.}
[4]
(iii)
Show that the point A{A} with coordinates (1,12,9){\left( - 1, 12, 9 \right)} lies on l.{l.}
Find the coordinates of the point B{B} which is the mirror image of A{A} in p.{p.}
[3]
(iv)
Find the area of triangle OAB,{OAB,} where O{O} is the origin, giving your answer to the nearest whole number.
[3]

Answer