Vectors Proof Questions
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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 marksOA⃗=a
\vec{OA} = \mathbf{a}
OA=a
OB⃗=b
\vec{OB} = \mathbf{b}
OB=b
P P\,P is the point on AB AB\,AB such that AP:PB=3:2AP:PB = 3:2AP:PB=3:2
OP⃗=k(2a+3b) \vec{OP} = k(2\mathbf{a} + 3\mathbf{b}) OP=k(2a+3b)How is the vector AB⃗\vec{AB}AB expressed using the position vectors OA⃗\vec{OA}OA and OB⃗\vec{OB}OB?
Vectors Proof Questions Revision Guide
Revision notes for CCEA GCSE Maths Vectors Proof Questions: explanations and worked examples.