In a parallelogram ABCD, what is AC + BD?

Question 43

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In a parallelogram $ABCD$ , what is $\overrightarrow{AC} + \overrightarrow{BD}$ ?

2\overrightarrow{AB}

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\vec{0}

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2\overrightarrow{AD}

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2\overrightarrow{DA}

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CorrectNot quiteAnswer C

Correct answer: C

Parallelogram law: $\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{AD}$ ; and by the triangle law, $\overrightarrow{BD} = \overrightarrow{AD} - \overrightarrow{AB}$ .
Adding, $\overrightarrow{AB}$ cancels: $\overrightarrow{AC} + \overrightarrow{BD} = 2\overrightarrow{AD}$ .

Worth noting

$2\overrightarrow{AB}$ takes $\overrightarrow{BD} = \overrightarrow{AB} - \overrightarrow{AD}$ , which is $\overrightarrow{DB}$ , the diagonal the other way.

Concept: The parallelogram law of addition
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsAddition, components and the section formula

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Ten questions from Vectors, at your own pace.

In a parallelogram ABCDABCDABCD, what is AC→+BD→\overrightarrow{AC} + \overrightarrow{BD}AC+BD?

Explanation

In a parallelogram $ABCD$ , what is $\overrightarrow{AC} + \overrightarrow{BD}$ ?