What is the Cartesian equation of the line through $(5, -2, 4)$ parallel to $3\hat{i} + 2\hat{j} - 8\hat{k}$ ?

\frac{x + 5}{3} = \frac{y - 2}{2} = \frac{z + 4}{-8}

Correct answerYour answer

\frac{x - 3}{5} = \frac{y - 2}{-2} = \frac{z + 8}{4}

Correct answerYour answer

\frac{x - 5}{3} = \frac{y + 2}{2} = \frac{z - 4}{-8}

Correct answerYour answer

\frac{x - 5}{5} = \frac{y + 2}{2} = \frac{z - 4}{4}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Through $(x_1, y_1, z_1)$ with direction ratios $a, b, c$ : $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$ .
Here $\frac{x - 5}{3} = \frac{y + 2}{2} = \frac{z - 4}{-8}$ .

Worth noting

Writing $x + 5$ uses the point's coordinates with the wrong sign.

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

What is the Cartesian equation of the line through (5,−2,4)(5, -2, 4)(5,−2,4) parallel to 3i^+2j^−8k^3\hat{i} + 2\hat{j} - 8\hat{k}3i^+2j^​−8k^?