Yes, they are all correct.
(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!