g10-08-01 · Syllabus supplement
Move the arrow without changing the vector
Must equal vectors start at the same point?
1 MIN · PREDICT ON PAPER
Move an arrow of displacement(3,2) to a different starting point. Predict its length and components.
Discuss or write first. No typed answer is required to continue.
Position changed; components and magnitude determine the vector.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
A free vector is determined by magnitude and direction, not by its position. Translation preserves its component differences.
Conditions: Use directed displacement. The zero vector has magnitude0 but no defined direction.
Mathematical justification: If both endpoints gain(t₁,t₂), their difference remains(B+t)−(A+t)=B−A.
1 MIN · EXIT CHECK
Are arrows from(0,0) to(2,−1) and(3,4) to(5,3) equal?
Check after answering
Yes, both have displacement(2,−1).
Teacher guidance and extension
Before: Coordinates, displacement and Pythagoras.
Ask: Which subtraction removes the common starting position?
Watch for: Calling two translated arrows different vectors because their endpoints differ.
Challenge: Explain why reversing the arrow usually changes the vector.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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