Kenneth ChengMathematical modeling
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Find the signed scalar projection of v onto u.

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 / Standard#Your turn

Find the signed scalar projection of v onto u.

v=(30,2,0), u=(1,0,0)v=(30,2,0),\ u=(1,0,0)
  • Projection requires a nonzero direction; signed scalar projection can be negative.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Use the dot product to connect coordinates with length or angle.
Hint 2
Use this intermediate relation.
s=v⋅u/∣u∣s=v\cdot u/|u|
Worked solution

  1. Use the dot product to connect coordinates with length or angle.

  2. Apply the stated relation and retain its conditions.

    s=30/1=30s=30/1=30

  3. A unit coordinate direction picks out the matching component.

The requested value is 30.

Checks and common pitfalls: A unit coordinate direction picks out the matching 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 ↗