Edit : Tutor confirmed the messy answer is correct.

In the assignment, Question 6 relies on correct answers for 4 and 5. I think I have made a small sign error somewhere, since the numbers are not typical of an assignment question otherwise.

Take a look at Q4 and Q5

Q6 requires me to find the intersection between both of those (the line L2 in Q4 and the plane in Q5)

I get down to a final bit that say 101t + 46 = 55 (to find t and then sub back in to the parametric equation)

This gives me t = 9/101

However, the fact that if the 46 was negative, it would be 101t = 55+46 would give me t = 1 is too obvious to ignore. So I think I should have 101t-46 = 55 but I can't see where I have gone wrong.

Attached is my working.

There is a small mistake in this one, the vector equation for s should be (-3,-1,2) but I wrote (-3,1,3) for some reason. However, in the system below that, you can see it is correct (ie, y = 2 -s -5t)