Question 1315

Vectors II: Lines and Planes
2015 Paper 2 Question 2 Variant

Question

The line L{L} has equation
r=(4ij3k)+λ(4i3j).\mathbf{r} = \left( - 4 \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \right) + \lambda \left( 4 \mathbf{i} - 3 \mathbf{j} \right).
(i)
Find the acute angle between L{L} and the x{x}-axis.
[2]
The point P{P} has position vector 6i+4j.{6 \mathbf{i} + 4 \mathbf{j}.}
(ii)
Find the points on L{L} which are a distance of 134{\sqrt{134}} from P.{P.}
Hence or otherwise find the point on L{L} which is closest to P.{P.}
[5]
(iii)
Find a cartesian equation of the plane that includes the line L{L} and the point P.{P.}
[3]

Answer