Which of these lines is perpendicular to the line (x - 2)/1 = (y + 3)/2 = (z - 1)/(-2)?

Question 61

EasyOriginal question

Which of these lines is perpendicular to the line $\frac{x - 2}{1} = \frac{y + 3}{2} = \frac{z - 1}{-2}$ ?

\frac{x}{2} = \frac{y - 1}{0} = \frac{z + 2}{1}

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

\frac{x}{1} = \frac{y}{1} = \frac{z}{1}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Perpendicular lines have $a_1a_2 + b_1b_2 + c_1c_2 = 0$ ; the given ratios are $1, 2, -2$ .
For $2, 0, 1$ : $2 + 0 - 2 = 0$ ; the other lines give $9$ , $-4$ and $1$ .

Worth noting

$\frac{x + 1}{1} = \frac{y}{2} = \frac{z - 3}{-2}$ has the same ratios as the given line: it is parallel, not perpendicular.

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