What is the Cartesian form of the line r = (2 i - j + 4 k) + λ( i + 2 j - k)?

(x - 2)/1 = (y + 1)/2 = (z - 4)/(-1)

(x - 1)/2 = (y - 2)/(-1) = (z + 1)/4

(x + 2)/1 = (y - 1)/2 = (z + 4)/(-1)

(x - 2)/1 = (y + 1)/2 = (z - 4)/1

Question 32

EasyOriginal question

What is the Cartesian form of the line $\vec{r} = (2\hat{i} - \hat{j} + 4\hat{k}) + \lambda(\hat{i} + 2\hat{j} - \hat{k})$ ?

\frac{x - 1}{2} = \frac{y - 2}{-1} = \frac{z + 1}{4}

Correct answerYour answer

\frac{x + 2}{1} = \frac{y - 1}{2} = \frac{z + 4}{-1}

Correct answerYour answer

\frac{x - 2}{1} = \frac{y + 1}{2} = \frac{z - 4}{1}

Correct answerYour answer

\frac{x - 2}{1} = \frac{y + 1}{2} = \frac{z - 4}{-1}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Worth noting

Swapping the point and the direction puts $1, 2, -1$ in the numerators.

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