Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, - 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

Solution:

(i) The coordinates of point R that divides the line segment joining the points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) internally in the ratio m : n are

[(mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n), (mz₂ + nz₁)/(m + n)]

Let R (x, y, z) be the point that divides the line segment joining points (- 2, 3, 5) and (1, - 4, 6) internally in the ratio 2 : 3

Hence,

x = (2(1) + 3(- 2))/(2 + 3), y = (2(- 4) + 3(3))/(2 + 3) and z = (2(6) + 3(5))/(2 + 3)

i.e., x = - 4/5, y = 1/5 and z = 27/5

Thus, the coordinates of the required point are (- 4/5, 1/5, 27/5).

(ii) The coordinates of point R that divides the line segment joining the points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) externally in the ratio m : n are

[(mx₂ - nx₁)/(m - n), (my₂ - ny₁)/(m - n), (mz₂ - nz₁)/(m - n)]

Let R (x, y, z) be the point that divides the line segment joining points (- 2, 3, 5) and (1, - 4, 6) internally in the ratio 2 : 3

Hence,

x = (2(1) - 3(- 2))/(2 - 3), y = (2(- 4) - 3(3))/(2 - 3) and z = (2(6) - 3(5))/(2 - 3)

i.e., x = - 8, y = 17 and z = 3

Thus, the coordinates of the required point are (- 8, 17, 3)

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NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.3 Question 1

Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, - 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally

Summary:

(i) The coordinates of the required point are (- 4/5, 1/5, 27/5)
(ii) The coordinates of the required point are (- 8, 17, 3)