LEARN · EXPLAIN · REVISE

Find the opposite vector.

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 / Standard#Your turn

\mathbf a=(3,-5)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

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

Hint 2

Negate both coordinates.

Worked solution

Separate magnitude, direction and position; compare vectors by displacement.
Calculate or simplify this relation.
$-\mathbf a=(-3,5);\quad\mathbf a+(-\mathbf a)=\mathbf0$
An opposite vector has the same magnitude and reversed direction.

(−3,5).

Checks and common pitfalls: An opposite vector has the same magnitude and reversed direction.

Reasoning checklist · self / teacher assessment

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.