Solve both parts and justify the conditions used. Part A: Explain why the sine rule in an SSA problem may give two triangles. Part B: Do equal magnitudes guarantee equal vectors? Give a counterexample.

01 / Standard#Your turn

Solve both parts and justify the conditions used. Part A: Explain why the sine rule in an SSA problem may give two triangles. Part B: Do equal magnitudes guarantee equal vectors? Give a counterexample.

\begin{gathered}\text{A: }\sin B=s,\quad0<s<1\\\text{B: }|\mathbf a|=|\mathbf b|=10\end{gathered}

Use the domain, units and sampling assumptions stated in the question.
Use the domain, units and sampling assumptions stated in the question.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

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

Hint 2

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

Worked solution

Part A reasoning
Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$\sin B=\sin(180^{\circ}-B)$
A supplementary candidate is discarded if the angle sum makes it impossible.
Part B reasoning
Separate magnitude, direction and position; compare vectors by displacement.
Calculate or simplify this relation.
$|(10,0)|=|(0,10)|=10$
The two perpendicular nonzero vectors cannot be equal.

A: Both B and 180°−B have the same sine; each must be checked against the remaining angle and side conditions. B: No: (10,0) and (0,10) have different directions.

Checks and common pitfalls: A supplementary candidate is discarded if the angle sum makes it impossible. The two perpendicular nonzero vectors cannot be equal.

Reasoning checklist · self / teacher assessment

Solve part A with its stated restrictions.
Solve part B using an appropriate representation.
Give the reasoning and check conditions in both parts.

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

Solve both parts and justify the conditions used. Part A: Explain why the sine rule in an SSA problem may give two triangles. Part B: Do equal magnitudes guarantee equal vectors? Give a counterexample.

Plane vectors and applications: mixed assessment

What you will be able to explain

Try it. Leave your reasoning visible.

Solve both parts and justify the conditions used. Part A: Explain why the sine rule in an SSA problem may give two triangles. Part B: Do equal magnitudes guarantee equal vectors? Give a counterexample.

Question sequence

Board plan

Anticipated thinking

Assessment checklist