Assertion (A): i × j = k and j × i = - k. Reason (R): Swapping the order of a vector product changes its sign.

Question 92

EasyOriginal question

Assertion (A): $\hat{i} \times \hat{j} = \hat{k}$ and $\hat{j} \times \hat{i} = -\hat{k}$ .
Reason (R): Swapping the order of a vector product changes its sign.

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

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

A is true: $\hat{i}, \hat{j}, \hat{k}$ form a right-handed system.
R is true and gives $\hat{j} \times \hat{i} = -(\hat{i} \times \hat{j})$ , the second half of A.

Concept: Order in the vector product
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsThe vector product

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Ten questions from Vectors, at your own pace.

Assertion (A): i^×j^=k^\hat{i} \times \hat{j} = \hat{k}i^×j^​=k^ and j^×i^=−k^\hat{j} \times \hat{i} = -\hat{k}j^​×i^=−k^.Reason (R): Swapping the order of a vector product changes its sign.

Explanation

Assertion (A): $\hat{i} \times \hat{j} = \hat{k}$ and $\hat{j} \times \hat{i} = -\hat{k}$ .
Reason (R): Swapping the order of a vector product changes its sign.