For any triangle ABC, what is AB + BC + CA?

Question 31

EasyOriginal question

For any triangle $ABC$ , what is $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA}$ ?

\vec{0}

Correct answerYour answer

2\overrightarrow{AC}

Correct answerYour answer

\overrightarrow{AC}

Correct answerYour answer

2\overrightarrow{CA}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Triangle law: $\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}$ .
$\overrightarrow{AC} + \overrightarrow{CA} = \vec{0}$ : the path ends where it began.

Worth noting

$2\overrightarrow{AC}$ treats $\overrightarrow{CA}$ as $\overrightarrow{AC}$ ; they point opposite ways.

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