Edexcel IGCSE Maths 复习笔记 5.1.3 Vectors - Proving Things

What are vector proofs?

• In vector proofs we use vectors, along with a few key ideas, to prove that things are true in geometrical diagrams

Parallel vectors

• Two vectors are parallel if and only if one is a multiple of the other
• This tends to appear in vector proofs in the following ways:

1. If you find in your workings that one vector is a multiple of the other, then you know that the two vectors are parallel – you can then use that fact in the rest of the proof

2. If you need to show that two vectors are parallel, then all you need to do is show that one of the vectors multiplied by some number is equal to the other one

Points on a straight line

• Often you are asked to show in a vector proof that three points lie on a straight line (ie that they are collinear)
• This is generally done as follows:

Vectors divided in ratios

• Be careful turning ratios into fractions in vector proofs!

4. If a point  divides a line segment  in the ratio p : q, then: 

eg. In the following diagram, the point  divides  in the ratio 3: 5: