LEARN · EXPLAIN · REVISE

Find the magnitude of the resultant force.

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

高一必修第二册(A版).pdf · 6.4 · PDF 45 / printed page 38

TOPIC 01

Applications of plane vectors

Build understanding of applications 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 F_1=(9,0),\quad\mathbf F_2=(0,12)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the geometry or physical quantity into vectors and check angle conventions.

Hint 2

Add forces as vectors before taking magnitude.

Worked solution

Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$|\mathbf F_1+\mathbf F_2|=\sqrt{81+144}=15$
Adding magnitudes directly is valid only for forces in the same direction.

The requested value is 15.

Checks and common pitfalls: Adding magnitudes directly is valid only for forces in the same direction.

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

Teacher preparation and assessment

Connect geometric and algebraic forms of applications of plane vectors.
Geometry: Vectors yield metric relations, sine and cosine rules, and triangle centres.
Physical quantities: Add forces as vectors; calculate work with a dot product.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Vectors yield metric relations, sine and cosine rules, and triangle centres.
Expected reasoning: Add forces as vectors; calculate work with a dot product.
Expected correction: An SSA triangle may have two valid configurations.