Which of these vectors has the same direction as 3 i - 6 j + 2 k?

Question 11

EasyOriginal question

Which of these vectors has the same direction as $3\hat{i} - 6\hat{j} + 2\hat{k}$ ?

-3\hat{i} + 6\hat{j} - 2\hat{k}

Correct answerYour answer

3\hat{i} + 6\hat{j} + 2\hat{k}

Correct answerYour answer

9\hat{i} - 18\hat{j} + 2\hat{k}

Correct answerYour answer

6\hat{i} - 12\hat{j} + 4\hat{k}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Same direction means a positive multiple: $\vec{b} = \lambda\vec{a}$ with $\lambda > 0$ .
$6\hat{i} - 12\hat{j} + 4\hat{k} = 2(3\hat{i} - 6\hat{j} + 2\hat{k})$ ; $-3\hat{i} + 6\hat{j} - 2\hat{k}$ is a negative multiple, and the other two are not multiples at all.

Worth noting

$-3\hat{i} + 6\hat{j} - 2\hat{k}$ is collinear, but its multiple is $-1$ : it points the opposite way.

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