How to quickly find the intersection between planes

Finding the intersection between planes is typically 4 marks in A level exam, and can be solved using this method in 1 min 🙂

For example, find the line of intersection of r. ( 1 1 0 )=3 and r.(-1 -1 2 )= 7

Basically, we are finding the solution of these two equations:

x+y = 3

-x-y+2z = 7

Use TI 84 plus calculator.

so we have

x= 3-y

y= y

z=5

So the line of intersection is r = (3 0 5) + a(- 1 1 0),  where a is a real number.