Further Mathematics

1. 1.

   Find the angle between the normals to planes x + 2y + 2z = 4 and 2x + y - 2z = 1.

   [3 marks] · no calculator
2. 2.

   Find where r = (1,0,2) + t(2,1,-1) meets x + y + z = 7.

   [3 marks] · no calculator
3. 3.

   Find a Cartesian equation of the plane through A = (1,0,0), B = (0,1,0), C = (0,0,2).

   [3 marks] · no calculator
4. 4.

   Find the perpendicular foot from P = (3,2,1) to plane x + 2y + 2z = 0, and the distance.

   [3 marks] · no calculator
5. 5.

   Lines L1: r = (0,0,0) + s(1,0,0) and L2: r = (0,1,1) + t(0,1,0). Show they are skew and find their shortest distance and closest points.

   [3 marks] · no calculator
6. 6.

   Find a vector equation of the intersection of x + y + z = 3 and x - y + z = 1. Find the point on that line nearest the origin.

   [3 marks] · no calculator

Original, unofficial practice questions from SubjectScout — not official past-paper questions.