Notation of lines in space Vector equation Parametric equations This can be made up from the vector equation: Make up the equations for y and z. coordinate on the line the vector part

Lines in space - questions 1. A line, L1, parallel to the vector 4i+2j-k passes through the coordinate (1,2,3). a) Write down the vector equation of the line L1. b) Write down the parametric equation of the line L1. 2. A straight line, L2, passes through the points A(2,5,-1) and B(5,-1,0). a) Find the vector AB. b) Hence write down the parametric equation of L2.

Shortest distance in space As before with closest distance from a point to a line is by making a path from the point to the line that will meet at a right angle. Vectors AB and PQ will meet at right angles. Example Find the shortest distance from the point P(-5,10,-6) to the line with parametric equations x=1-3t,y=4+2t,z=1-4t. B Q A P(-5,10,-6) If t=2 then Q(-5,8,-7). Let Q be where the lines meet. Q will have the coordinates: (1-3t, 4+2t, 1-4t)