Kenneth ChengMathematical modeling
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Do equal magnitudes guarantee equal vectors? Give a counterexample.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Plane vectors and applications: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

Do equal magnitudes guarantee equal vectors? Give a counterexample.

∣a∣=∣b∣=10|\mathbf a|=|\mathbf b|=10
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Separate magnitude, direction and position; compare vectors by displacement.
Hint 2
Equality requires both length and direction.
Worked solution

  1. Separate magnitude, direction and position; compare vectors by displacement.

  2. Calculate or simplify this relation.

    ∣(10,0)∣=∣(0,10)∣=10|(10,0)|=|(0,10)|=10

  3. The two perpendicular nonzero vectors cannot be equal.

No: (10,0) and (0,10) have different directions.

Checks and common pitfalls: The two perpendicular nonzero vectors cannot be equal.

Reasoning checklist · self / teacher assessment
  • State the relevant definition, condition or model.
  • Show a valid calculation, proof or counterexample.
  • Interpret the conclusion with its restrictions.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗