Kenneth ChengMathematical modeling
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Find the first component of a+b.

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

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TOPIC 01

Space vectors and solid geometry: mixed review

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

Find the first component of a+b.

a=(24,2,−1),b=(3,−2,4)a=(24,2,-1),\quad b=(3,-2,4)
  • The angle formula requires two nonzero vectors; a dot product is a scalar.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Use vector components and the distributive laws.
Hint 2
Use this intermediate relation.
(a+b)1=a1+b1(a+b)_1=a_1+b_1
Worked solution

  1. Use vector components and the distributive laws.

  2. Apply the stated relation and retain its conditions.

    (a+b)=(27,0,3)(a+b)=(27,0,3)

  3. Cancellation of other components does not affect the first component.

The requested value is 27.

Checks and common pitfalls: Cancellation of other components does not affect the first component.

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 ↗