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Vectors proof questions turn a diagram into algebra. The first job is to write important position vectors from the origin, usually in terms of aaa and bbb.
A side vector is found by subtracting position vectors in the correct order. The key route fact is
AB⃗=OB⃗−OA⃗ \vec{AB}=\vec{OB}-\vec{OA} AB=OB−OASo if OA⃗=4a\vec{OA}=4aOA=4a and OB⃗=3b\vec{OB}=3bOB=3b, then
AB⃗=3b−4a,BA⃗=4a−3b \vec{AB}=3b-4a,\qquad \vec{BA}=4a-3b AB=3b−4a,BA=4a−3bReversing the direction changes the sign, so order always matters.
Question 1
4 marksP is the point on AB AB\,AB such that AP:PB=1:3AP:PB = 1:3AP:PB=1:3
OP⃗=k(3a+b) \vec{OP} = k(3\mathbf{a} + \mathbf{b}) OP=k(3a+b)How is the vector AB⃗\vec{AB}AB expressed using the position vectors OA⃗\vec{OA}OA and OB⃗\vec{OB}OB?
Revision notes for Edexcel GCSE Maths Vectors Proof Questions. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.
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The position vectors of A and B are 2a2a2a and 5b5b5b. What is the directed vector AB\text{AB}AB?
