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Vectors · Question 49 of 125

What is the length of the diagonal BD?

Question 49

MediumOriginal question

Three vertices of a parallelogram $ABCD$ , taken in order, are $A(1, 2, -1)$ , $B(2, -1, 0)$ and $C(5, 4, 3)$ .

What is the length of the diagonal $BD$ ?

6

Correct answerYour answer

6 \sqrt{2}

Correct answerYour answer

2 \sqrt{19}

Correct answerYour answer

72

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\overrightarrow{BD} = \vec{d} - \vec{b} = 2\hat{i} + 8\hat{j} + 2\hat{k}$ .
$\lvert \overrightarrow{BD} \rvert = \sqrt{4 + 64 + 4} = \sqrt{72} = 6\sqrt{2}$ .

Worth noting

$2\sqrt{19}$ adds the position vectors of $B$ and $D$ instead of subtracting them.

Concept: The vector joining two points
Typical timeTypical: 120 s
Your timeYours: —

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