What is ( i + 2 j - k) × (2 i - j + 3 k)?

Question 106

MediumOriginal question

What is $(\hat{i} + 2\hat{j} - \hat{k}) \times (2\hat{i} - \hat{j} + 3\hat{k})$ ?

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

Correct answerYour answer

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

Correct answerYour answer

7\hat{i} - 5\hat{j} - 5\hat{k}

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\hat{i}(2 \cdot 3 - (-1)(-1)) - \hat{j}(1 \cdot 3 - (-1) \cdot 2) + \hat{k}(1 \cdot (-1) - 2 \cdot 2)$ .
$= 5\hat{i} - 5\hat{j} - 5\hat{k}$ .

Worth noting

$-5\hat{i} + 5\hat{j} + 5\hat{k}$ is $\vec{b} \times \vec{a}$ , the product in the other order.

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