Date | May 2021 | Marks available | 2 | Reference code | 21M.2.AHL.TZ1.6 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
Consider the planes Π1 and Π2 with the following equations.
Π1: 3x+2y+z=6
Π2: x-2y+z=4
Find a Cartesian equation of the plane Π3 which is perpendicular to Π1 and Π2 and passes through the origin (0, 0, 0).
Find the coordinates of the point where Π1, Π2 and Π3 intersect.
Markscheme
attempt to find a vector perpendicular to Π1 and Π2 using a cross product (M1)
(321)×(1-21)=(2-(-2))i+(1-3)j+(-6-2)k
=(4-2-8)(=2(2-1-4)) (A1)
equation is 4x-2y-8z=0(⇒2x-y-4z=0) A1
[3 marks]
attempt to solve 3 simultaneous equations in 3 variables (M1)
(4121, -1021, 2321)(=(1.95, -0.476, 1.10)) A1
[2 marks]