Vector distance questions are common in alevel and carries 5 or 6 marks. Knowing the vector distance formulas can help to solve such questions easily and quickly.
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
So the line of intersection is r = (3 0 5) + a(- 1 1 0), where a is a real number.