NCERT Solutions class-11 Maths Exercise 12.3

Exercise 12.3

1. Find the coordinates of the point which divides the line segment joining the points and in the ratio:

(i) 2: 3 internally,

(ii) 2: 3 externally.

Ans. (i) Let P be any point which divides the line segment joining points A

and B in the ratio 2: 3 internally. Then

Therefore, Coordinates of P are

(ii) Let P be any point which divides the line segment joining points A and B in the ratio 2: 3 externally. Then

Therefore, Coordinates of P are

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2. Given that P Q and Rare collinear. Find the ratio in which Q divides PR.

Ans. Let Q divides the line segment joining points P and R in the ratio internally. Then

Coordinates of Q are

According to question,

Therefore, Q divides the line segment joining the points P and R in the ratio 1: 2.

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3. Find the ratio in which the YZ-plane divides the line segment formed by joining the points and

Ans. Let the line segment joining points A and B be divided by YZ-plane at a point C in the ratio internally. Then

Coordinates of C are

According to question, C lies on YZ-plane, i.e.,

Therefore, the required ratio is 2: 3.

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4. Using section formula, show that the points A B and C are collinear.

Ans. Let the points B divides the line segment joining A and C in the ratio internally.

Then coordinates of B =

Now

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5. Find the coordinates of the points which trisect the line segment joining the points P and Q

Ans. Let R and S be two points which trisect the line segment PQ.

Then PR = RS = SQ

Point R divides the lines segment PQ in the ratio 1: 2.

Then Coordinates of R = =

Again, Point S divides the line segment PQ in the ratio 2: 1.

Then Coordinates of S = =