P is (1, 2, 0) and Q is (7, -4, 6). Match each point in List I with its coordinates in List II. | List I | List II | |---|---| | A. The midpoint of PQ | I. (-5, 8, -6) | | B. The point dividing PQ internally in the ratio 2 : 1 | II. (13, -10, 12) | | C. The point dividing PQ externally in the ratio 2 : 1 | III. (5, -2, 4) | | D. The point dividing PQ externally in the ratio 1 : 2 | IV. (4, -1, 3) |

P is (1, 2, 0) and Q is (7, -4, 6). — CUET Maths practice

P is (1, 2, 0) and Q is (7, -4, 6).

Question 57

HardOriginal question

$P$ is $(1, 2, 0)$ and $Q$ is $(7, -4, 6)$ . Match each point in List I with its coordinates in List II.

List I	List II
A. The midpoint of $PQ$	I. $(-5, 8, -6)$
B. The point dividing $PQ$ internally in the ratio 2 : 1	II. $(13, -10, 12)$
C. The point dividing $PQ$ externally in the ratio 2 : 1	III. $(5, -2, 4)$
D. The point dividing $PQ$ externally in the ratio 1 : 2	IV. $(4, -1, 3)$

A-IV, B-III, C-I, D-IICorrect answerYour answerA-III, B-IV, C-II, D-ICorrect answerYour answerA-IV, B-II, C-III, D-ICorrect answerYour answerA-IV, B-III, C-II, D-ICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Internally in $m : n$ : $\frac{m\vec{q} + n\vec{p}}{m + n}$ ; externally: $\frac{m\vec{q} - n\vec{p}}{m - n}$ .
A is $(4, -1, 3)$ . B: $\frac{2(7, -4, 6) + (1, 2, 0)}{3} = (5, -2, 4)$ . C: $2(7, -4, 6) - (1, 2, 0) = (13, -10, 12)$ . D: $\frac{(7, -4, 6) - 2(1, 2, 0)}{-1} = (-5, 8, -6)$ .

Worth noting

The two external points differ: 2 : 1 lies beyond $Q$ , and 1 : 2 lies beyond $P$ .

Concept: The section formula
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsAddition, components and the section formula

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Ten questions from Vectors, at your own pace.

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Ten questions from Vectors, at your own pace.

P is (1, 2, 0) and Q is (7, -4, 6).

Question 57

Explanation