The point $R(3, 1, 0)$ divides $PQ$ internally in the ratio 2 : 3, and $P$ is $(1, -1, 2)$ . What is $Q$ ?

(\frac{13}{3}, \frac{7}{3}, - \frac{4}{3})

Correct answerYour answer

(5, 3, -2)

Correct answerYour answer

(6, 4, -3)

Correct answerYour answer

(9, 1, 3)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\vec{r} = \frac{2\vec{q} + 3\vec{p}}{5}$ , so $\vec{q} = \frac{5\vec{r} - 3\vec{p}}{2}$ .
$\frac{5(3, 1, 0) - 3(1, -1, 2)}{2} = \frac{(12, 8, -6)}{2} = (6, 4, -3)$ .

Worth noting

$(\frac{13}{3}, \frac{7}{3}, - \frac{4}{3})$ puts the weight 2 on $P$ instead of on $Q$ .

Ten questions from Vectors, at your own pace.

The point R(3,1,0)R(3, 1, 0)R(3,1,0) divides PQPQPQ internally in the ratio 2 : 3, and PPP is (1,−1,2)(1, -1, 2)(1,−1,2). What is QQQ?