Question 1312

Vectors II: Lines and Planes
2012 Paper 1 Question 9 Variant

Question

(i)
Find a vector equation of the line through the points A{A} and B{B} with position vectors 4i5j+5k{4 \mathbf{i} - 5 \mathbf{j} + 5 \mathbf{k}} and i8j+8k{\mathbf{i} - 8 \mathbf{j} + 8 \mathbf{k}} respectively.
[3]
(ii)
The perpendicular to this line from the point C{C} with position vector 3i6j{3 \mathbf{i} - 6 \mathbf{j}} meets the line at the point N.{N.} Find the position vector of N{N} and the ratio AN:NB.{AN:NB.}
[5]
(iii)
Find the cartesian equation of the line which is a reflection of the line AC{AC} in the line AB.{AB.}
[4]

Answer