What is the Cartesian equation of the line through $(3, -2, -5)$ and $(3, -2, 6)$ ?

\frac{x - 3}{6} = \frac{y + 2}{-4} = \frac{z + 5}{1}

Correct answerYour answer

\frac{x}{3} = \frac{y}{-2} = \frac{z - 11}{-5}

Correct answerYour answer

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

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\frac{x - 3}{0} = \frac{y + 2}{0} = \frac{z + 5}{11}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Direction ratios $B - A = 0, 0, 11$ .
So $\frac{x - 3}{0} = \frac{y + 2}{0} = \frac{z + 5}{11}$ ; the zero denominators mean $x = 3$ , $y = -2$ all along the line.

Worth noting

Adding the points' coordinates gives no direction; the direction is their difference.

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

What is the Cartesian equation of the line through (3,−2,−5)(3, -2, -5)(3,−2,−5) and (3,−2,6)(3, -2, 6)(3,−2,6)?