What is b₁ × b₂?

Question 96

MediumOriginal question

Two lines are $L_1: \vec{r} = (\hat{i} + 2\hat{k}) + \lambda(\hat{i} + 2\hat{j} - \hat{k})$ and $L_2: \vec{r} = (\hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + \hat{k})$ .

What is $\vec{b_1} \times \vec{b_2}$ ?

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

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

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

Worth noting

$-3\hat{i} + 3\hat{j} + 3\hat{k}$ is $\vec{b_2} \times \vec{b_1}$ , the product in the other order.

Concept: The common perpendicular direction
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsSkew lines and the shortest distance

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Ten questions from Three-Dimensional Geometry, at your own pace.

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Ten questions from Three-Dimensional Geometry, at your own pace.

What is b₁ × b₂?

Question 96

Explanation