Assertion (A): For non-zero vectors a and b, if | a + b | = | a - b |, then a is perpendicular to b. Reason (R): | a + b |^2 - | a - b |^2 = 4 a · b.

Question 80

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Assertion (A): For non-zero vectors $\vec{a}$ and $\vec{b}$ , if $\lvert \vec{a} + \vec{b} \rvert = \lvert \vec{a} - \vec{b} \rvert$ , then $\vec{a}$ is perpendicular to $\vec{b}$ .
Reason (R): $\lvert \vec{a} + \vec{b} \rvert^{2} - \lvert \vec{a} - \vec{b} \rvert^{2} = 4\vec{a} \cdot \vec{b}$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

R: the squares are $\lvert \vec{a} \rvert^{2} \pm 2\vec{a} \cdot \vec{b} + \lvert \vec{b} \rvert^{2}$ , and their difference is $4\vec{a} \cdot \vec{b}$ . True.
A: equal magnitudes make the left side of R zero, so $\vec{a} \cdot \vec{b} = 0$ and the non-zero vectors are perpendicular. R is the reason.

Concept: Perpendicular sum and difference
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe scalar product

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