(a) The position vectors of the points A and B, relative to a fixed origin O, are i + 3j – 2k and

3i + 6j + k, respectively.

(i) Find AB.

(ii) Find the vector equation of the line AB.

(iii) The vector equation of the line L is r = 2i + 3j + 7k + μ (i + j + 4k).

Given that L and AB intersect, find the position vector of the point of intersection. [9]

(b) Find the angle between the vectors i + 2j – k and 3i – j + 2k. [6]

For AB I have 2i + 3j + 3k

and the vector equation is i+3j-2k + t(2i+3j+3k).

For the position vector at the point of intersection I have -i - 5k.

For the angle between the vectors I have 96.3 degrees.

Have I done all of this correctly? Thank you very much if you can check my answers!