LEARN · EXPLAIN · REVISE

A walker travels 2 m east then 2 m west. Find the magnitude of displacement.

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

高一必修第二册(A版).pdf · 6.1 · PDF 9 / printed page 2

TOPIC 01

Concept of plane vectors

Build understanding of concept of plane vectors through definitions, contrasting cases and justified applications.

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

01 / Transfer#Worked example

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

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

Hint 2

Displacement depends only on start and finish.

Worked solution

The requested value is 0.

Checks and common pitfalls: The distance travelled is 4 m, although displacement is zero.

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

Teacher preparation and assessment

Connect geometric and algebraic forms of concept of plane vectors.
Magnitude and direction: A nonzero vector has length and direction, independent of where it is drawn.
Zero and unit vectors: Zero has magnitude zero; a unit vector has magnitude one.
Close with: conditions → representation → reasoning → check.

Expected reasoning: A nonzero vector has length and direction, independent of where it is drawn.
Expected reasoning: Zero has magnitude zero; a unit vector has magnitude one.
Expected correction: Equal lengths do not imply equal vectors.