Is this all correct? (more bl**dy vectors!) I hope these are right, but I have the nagging suspicion that they're not? Where have I gone wrong (if I have indeed gone wrong)? 1. The problem statement, all variables and given/known data line P has equation (x+3)/2 = y = z-1 (a) Show that point Q (2,1,2) does not lie on line P. (b) Write down the parametric equations for the line. (c) Use dot product properties to find the co-ords of point R which is on P, such that QR is perpendicular to P. 3. The attempt at a solution (a) sub (2,1,2) into the equation: (2+3)/2 = 1 = 2-1 5/2 = 1 = 1 they don't equal, therefore point Q does not lie on line P. Is it that simple, or do I need to use [v(P) = (-3,0,1) + t(2,1,1)] and the parametric equations such that x=2t-3=2, y=t=1 & z=t+1=2 and attempt a solution. Here it is inconsistent. (b) parametric equations: x=2t-3 y=t z=t-1 (c) dot product: let u = (2,1,2) and v=(-3,0,1) u.v = (2 1 2).(-3 0 1) |i 2 -3 | = det |j 1 0 | = i - 8j + 3k |k 2 1 | point R = (1, -8, 3). again, I feel I've skipped a step here, but it's 11.30pm and I'm too tired to think any further! many thanks in advance! I'll be checking again in the am.