g10-08-02 · Syllabus supplement
A detour and its final displacement
Does changing the order of two displacements change the destination?
1 MIN · PREDICT ON PAPER
Compare a+b andb+a for a=(2,1),b=(−1,3).
Discuss or write first. No typed answer is required to continue.
The resultant joins the original start to the final endpoint.
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
Vector addition joins arrows head-to-tail and adds components. Subtraction adds the opposite arrow; path length is a different quantity.
Conditions: All arrows use the same coordinate scale. Resultant magnitude need not equal the sum of magnitudes.
Mathematical justification: (a₁+b₁,a₂+b₂)=(b₁+a₁,b₂+a₂) by commutativity of real addition. Subtraction uses a+(−b).
1 MIN · EXIT CHECK
Find(2,1)−(−1,3).
Check after answering
(3,−2).
Teacher guidance and extension
Before: Coordinates, displacement and Pythagoras.
Ask: Which arrow shows the trip, and which joins the first start to the final end?
Watch for: Adding lengths while ignoring direction.
Challenge: Construct a trip with positive distance but zero displacement.
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.
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