What is the vector of magnitude 9 in the direction of $2\hat{i} + \hat{j} - 2\hat{k}$ ?

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

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\lvert 2\hat{i} + \hat{j} - 2\hat{k} \rvert = 3$ , so the unit vector is $\frac{1}{3}(2\hat{i} + \hat{j} - 2\hat{k})$ .
$9 \times \frac{1}{3}(2\hat{i} + \hat{j} - 2\hat{k}) = 6\hat{i} + 3\hat{j} - 6\hat{k}$ .

Worth noting

$18\hat{i} + 9\hat{j} - 18\hat{k}$ multiplies by 9 without first making the vector a unit vector; its magnitude is 27.

Ten questions from Vectors, at your own pace.

What is the vector of magnitude 9 in the direction of 2i^+j^−2k^2\hat{i} + \hat{j} - 2\hat{k}2i^+j^​−2k^?