What are the direction cosines of the line joining $P(1, 2, -3)$ and $Q(3, 1, -1)$ , directed from $P$ to $Q$ ?

2, -1, 2

Correct answerYour answer

\frac{2}{3}, -\frac{1}{3}, \frac{2}{3}

Correct answerYour answer

-\frac{2}{3}, \frac{1}{3}, -\frac{2}{3}

Correct answerYour answer

\frac{2}{9}, -\frac{1}{9}, \frac{2}{9}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Direction ratios: $3 - 1, 1 - 2, -1 + 3 = 2, -1, 2$ , with $\sqrt{4 + 1 + 4} = 3$ .
Direction cosines: $\frac{2}{3}, -\frac{1}{3}, \frac{2}{3}$ .

Worth noting

$-\frac{2}{3}, \frac{1}{3}, -\frac{2}{3}$ points from $Q$ to $P$ , the other way.

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

What are the direction cosines of the line joining P(1,2,−3)P(1, 2, -3)P(1,2,−3) and Q(3,1,−1)Q(3, 1, -1)Q(3,1,−1), directed from PPP to QQQ?