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Vectors · Question 96 of 125

What is the area of the parallelogram?

Question 96

EasyOriginal question

A parallelogram has adjacent sides $\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} + 3\hat{j} - 2\hat{k}$ .

What is the area of the parallelogram?

3 square unitsCorrect answerYour answer6 square unitsCorrect answerYour answer12 square unitsCorrect answerYour answer144 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The area is $\lvert \vec{a} \times \vec{b} \rvert$ .
$\sqrt{64 + 64 + 16} = \sqrt{144} = 12$ .

Worth noting

6 halves the vector product, which gives the triangle on $\vec{a}$ and $\vec{b}$ , not the parallelogram.

Concept: Area from a vector product
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe vector product

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