Solve both parts and justify the conditions used. Part A: Simplify using the triangle rule. Part B: Find the x-coordinate of the centroid.

01 / Transfer#Your turn

\begin{gathered}\text{A: }\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}\\\text{B: }A=(0,0),\quad B=(21,0),\quad C=(0,3)\end{gathered}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

A: Use the vector operation law and preserve vector versus scalar types.

Hint 2

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

Worked solution

Part A reasoning
Use the vector operation law and preserve vector versus scalar types.
Calculate or simplify this relation.
$\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC};\quad\overrightarrow{AC}+\overrightarrow{CA}=\mathbf0$
Returning to the start gives zero total displacement.
Part B reasoning
Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$G=(A+B+C)/3=(7,1)$
The centroid lies two-thirds along each median from the vertex.

A: The zero vector. B: The requested value is 7.

Checks and common pitfalls: Returning to the start gives zero total displacement. The centroid lies two-thirds along each median from the vertex.

Reasoning checklist · self / teacher assessment

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

Plane vectors and applications: mixed assessment