What is the vector equation of the line through the origin and the point $(2, -1, 3)$ ?

\vec{r} = \lambda(2\hat{i} - \hat{j} + 3\hat{k})

Correct answerYour answer

\vec{r} = 2\hat{i} - \hat{j} + 3\hat{k}

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\vec{r} = \lambda(2\hat{i} + \hat{j} + 3\hat{k})

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\vec{r} = (2\hat{i} - \hat{j} + 3\hat{k}) + \lambda\hat{k}

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The line passes through $\vec{0}$ with direction $2\hat{i} - \hat{j} + 3\hat{k} - \vec{0}$ .
$\vec{r} = \vec{0} + \lambda(2\hat{i} - \hat{j} + 3\hat{k})$ .

Worth noting

$\vec{r} = 2\hat{i} - \hat{j} + 3\hat{k}$ has no parameter, so it is a single point.

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

What is the vector equation of the line through the origin and the point (2,−1,3)(2, -1, 3)(2,−1,3)?