1. Determine equation of the line in
a) The line through the points (7,-3,1) and (-2,1,4).
b) The line through the point (1,-5,0) and parallel to the line given by r (t)=(8–3t,-10+9t,-1-t)
c) The line through the point (1,-7, 14) and parallel to the line given by x = 6t, y =9, z = 8-16t /12
2. Determine the intersection point of the two lines or show that they do not intersect.
a) The line passing through the points (0,-9,-1) and (1,6,-3) and the line given by F(t)=(-9-4t, 10+6t, 1–2t).
b. The line given by x = 1+6t, y = -1–3t, z = 4+12t and the line given by x = 4+t, y = -10-8t, z=3-5t.
c. The line given by r (t)=(14+5t, -3t, 1+7t) and the line given by r(t) =(3-3t, 5+2t, -2+4t).
d. Does the line passing through (-5,4,-1) and (-3,-5,0) intersect the yz-plane? If so, give the point.
e. Does the line given by r (t) =(6+t, -8+14t, 4t) intersect the xz-plane? If so, give the point.
3. Which of the following points lies on the line x = 2t, y = 3, z = 1 + t
a) A(2,4,2) B(-2, 2 1) C(4, 5, 2) D(6,6,2) (4marks) b) If the point (a, b, -3) lies on the line, determine the values of a and b.
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