Question 5 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry (Important Question)
Last updated at April 16, 2024 by Teachoo
Chapter 12 Class 11 Introduction to Three Dimensional Geometry
Chapter 12 Class 11 Introduction to Three Dimensional Geometry
Last updated at April 16, 2024 by Teachoo
Question 5 Find the coordinates of the points which trisect the line segment joining the points P (4, 2, –6) and Q (10, –16, 6). Let Point A (a, b, c) & point B (p, q, r) trisect the line segment PQ i.e. PA = AB = BC Point A divides PQ in the ratio of 1 : 2 We know that , Coordinate of point that divides the line segment joining A(x1, y1, z1) & B(x2, y2, z2) internally in the ratio m: n is P(x, y, z) = ((〖𝑚 𝑥〗_2 +〖 𝑛 𝑥〗_1)/(𝑚 + 𝑛),(〖𝑚 𝑦〗_2 +〖 𝑛 𝑦〗_1)/(𝑚 + 𝑛),(〖𝑚 𝑧〗_2 +〖 𝑛 𝑧〗_1)/(𝑚 + 𝑛)) Here, m = 1 , n = 2 x1 = 4 , y1 = 2 , z1 = –6 x2 = 10 , y2 = –16 , z2 = 6 Coordinate of A are (a, b, c) = ((10 (1) + 4 (2))/(1 + 2),(−16 (1) + 2 (2))/(1 + 2),(6 (1) + (− 6) (2))/(1 + 2)) (a, b, c) = ((10 + 8)/3,(− 16 + 4)/3,(6 − 12)/3) (a, b, c) = (6, –4, –2) Hence, coordinates of A = (6, –4, –2) Now, Point B (p, q, r) divides AQ in the ratio 1 : 1 So, B is mid-point of AQ Coordinates of B = ((𝑥_(1 )+ 𝑥_2)/2,(𝑦_(1 )+ 𝑦_2)/2,(𝑧_(1 )+ 𝑧_2)/2) = ((6 + 10)/2,(−4 + (−16))/2,(−2 + 6)/2) = (160/2,(−20)/2,4/2) = (8, –10, 2) Hence coordinate of Point B = (8, –10, 2)