Which of these equations describes the same line as (x - 2)/2 = (y - 1)/3 = (z + 3)/(-1)?

(x - 6)/(-4) = (y - 7)/(-6) = (z + 5)/2

(x + 2)/2 = (y + 1)/3 = (z - 3)/(-1)

(x - 2)/4 = (y - 1)/6 = (z + 3)/2

(x - 6)/2 = (y - 7)/3 = (z + 4)/(-1)

Question 57

HardOriginal question

Which of these equations describes the same line as $\frac{x - 2}{2} = \frac{y - 1}{3} = \frac{z + 3}{-1}$ ?

\frac{x + 2}{2} = \frac{y + 1}{3} = \frac{z - 3}{-1}

Correct answerYour answer

\frac{x - 6}{-4} = \frac{y - 7}{-6} = \frac{z + 5}{2}

Correct answerYour answer

\frac{x - 2}{4} = \frac{y - 1}{6} = \frac{z + 3}{2}

Correct answerYour answer

\frac{x - 6}{2} = \frac{y - 7}{3} = \frac{z + 4}{-1}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Two equations give the same line when the directions are parallel and a point is shared: $-4, -6, 2 = -2(2, 3, -1)$ .
And $(6, 7, -5)$ is on the given line: $\frac{6 - 2}{2} = \frac{7 - 1}{3} = \frac{-5 + 3}{-1} = 2$ .

Worth noting

$\frac{x + 2}{2} = \frac{y + 1}{3} = \frac{z - 3}{-1}$ has the right direction but passes through $(-2, -1, 3)$ , which is not on the line.

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