Which pair of vectors is perpendicular?

2\hat{i} - \hat{j} + 3\hat{k}

and

\hat{i} + 5\hat{j} + \hat{k}

Correct answerYour answer

\hat{i} + 2\hat{j} - \hat{k}

and

2\hat{i} - \hat{j} + \hat{k}

Correct answerYour answer

3\hat{i} + \hat{j}

and

\hat{i} + 3\hat{j}

Correct answerYour answer

\hat{i} - \hat{j} + \hat{k}

and

-\hat{i} + \hat{j} - \hat{k}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Two non-zero vectors are perpendicular exactly when their scalar product is 0.
$2(1) + (-1)(5) + 3(1) = 2 - 5 + 3 = 0$ ; the other pairs give $-1$ , $6$ and $-3$ .

Worth noting

For $\hat{i} + 2\hat{j} - \hat{k}$ and $2\hat{i} - \hat{j} + \hat{k}$ the $\hat{i}$ and $\hat{j}$ products cancel, but the $\hat{k}$ product $-1$ remains.

Concept: Perpendicular vectors
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsThe scalar product

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Which pair of vectors is perpendicular?

Explanation