Question

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.

Class X1 - Maths -Introduction to Three Dimensional Geometry Page 277

Answer 1

(i) Let C divides the Line internally in the ratio 2 : 3
use section formula,
C≡ [ (mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)//, (mz₂ + nz₁)/(m + n)]
C ≡ [ (2 × 1 + 3 × -2)/(2 + 3), (2 × -4 + 3 × 3)/(2 + 3), (2 × 6 + 3 × 5)/(2 + 3)]
C≡ [ (2 - 6)/5 , ( -8 + 9)/5 , (12 + 15)/5 ]
C≡ [ -2/5, 1/5, 27/5 ]

(ii) Let C divides the Line externally in the ratio 2 : 3
C = [ (mx₂ - nx₁)/( m - n), (my₂ - ny₁)/(m - n), (mz₂ - nz₁)/(m -n) ]
C = [ (2 × 1 - 3 × -2)/(2 - 3), (2 × -4 -3 × 3)/( 2 - 3), (2 × 6 + 3 × 5)/( 2 - 3) ]
C = [ (2 + 6)/-1 , ( -8-9)/-1 , ( 12 - 15)/-1 ]
C = [ -8 , 17, 3 ]