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studyVectors, Matrices & Sets
AdvancedMaths revision

Vectors (2D)

Use vector components, magnitude and linear combinations to represent geometry and displacement.

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Focus points
✓Add and scale vectors.
✓Use vector magnitudes.
✓Prove geometric relationships with vectors.
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The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · vector addition
Given a=(3,−2) and b=(1,5), find a+b.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · linear combination
Find 2a−3b for a=(4,1), b=(−2,3).
Question 3FluencyCore
Original practice · Free Online Revision
Skill · magnitude
Find |(6,8)|.
Question 4FluencyCore
Original practice · Free Online Revision
Skill · unit vector
Find a unit vector in direction (3,4).
Question 5FluencyCore
Original practice · Free Online Revision
Skill · position vectors
Points A(1,2), B(5,7). Find vector AB.
Question 6FluencyCore
Original practice · Free Online Revision
Skill · vector path
A→B=a and B→C=b. Express A→C.
Question 7ReasoningCore
Original practice · Free Online Revision
Skill · midpoint vector
If OA=a and OB=b, express the midpoint M of AB as a position vector.
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · vector proof
In triangle OAB, M is midpoint of OA and N midpoint of OB. Prove MN is parallel to AB and half its length.