Which of the following statements are true? I. i · i = 1 and i · j = 0. II. a · b = b · a. III. If a · b = 0, then a = 0 or b = 0. IV. a · a = | a |^2.

Question 70

MediumOriginal question

Which of the following statements are true?
I. $\hat{i} \cdot \hat{i} = 1$ and $\hat{i} \cdot \hat{j} = 0$ .
II. $\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}$ .
III. If $\vec{a} \cdot \vec{b} = 0$ , then $\vec{a} = \vec{0}$ or $\vec{b} = \vec{0}$ .
IV. $\vec{a} \cdot \vec{a} = \lvert \vec{a} \rvert^{2}$ .

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

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CorrectNot quiteAnswer D

Correct answer: D

I, II and IV are properties of the dot product.
III is false: $\hat{i} \cdot \hat{j} = 0$ with neither vector zero; they are perpendicular.

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

The rule this testsThe scalar product

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