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Give a unit vector in the same direction.

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

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 / Foundation#Your turn

Give a unit vector in the same direction.

a=(24,32)\mathbf a=(24,32)
  • 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
Divide by the positive magnitude.
Worked solution
  1. Separate magnitude, direction and position; compare vectors by displacement.

  2. Calculate or simplify this relation.

    a∣a∣=(3/5,4/5)\frac{\mathbf a}{|\mathbf a|}=(3/5,4/5)
  3. Normalizing a zero vector would be undefined.

(3/5,4/5).

Checks and common pitfalls: Normalizing a zero vector would be undefined.

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 ↗