Which of the following statements are true? I. i × j = k and j × i = - k. II. a × a = 0 for every a. III. a × b = b × a. IV. a × b is perpendicular to both a and b.

Question 100

MediumOriginal question

Which of the following statements are true?
I. $\hat{i} \times \hat{j} = \hat{k}$ and $\hat{j} \times \hat{i} = -\hat{k}$ .
II. $\vec{a} \times \vec{a} = \vec{0}$ for every $\vec{a}$ .
III. $\vec{a} \times \vec{b} = \vec{b} \times \vec{a}$ .
IV. $\vec{a} \times \vec{b}$ is perpendicular to both $\vec{a}$ and $\vec{b}$ .

I, II and IV onlyCorrect answerYour answerAll four: I, II, III and IVCorrect answerYour answerI and IV onlyCorrect answerYour answerII, III and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I, II and IV are properties of the vector product.
III is false: $\vec{a} \times \vec{b} = -(\vec{b} \times \vec{a})$ ; the order matters.

Worth noting

The scalar product commutes; the vector product changes sign.

Concept: Properties of the vector product
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe vector product

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