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, โ6) and Q (10, โ16, 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) = ((ใ๐ ๐ฅใ_2 +ใ ๐ ๐ฅใ_1)/(๐ + ๐),(ใ๐ ๐ฆใ_2 +ใ ๐ ๐ฆใ_1)/(๐ + ๐),(ใ๐ ๐งใ_2 +ใ ๐ ๐งใ_1)/(๐ + ๐)) Here, m = 1 , n = 2 x1 = 4 , y1 = 2 , z1 = โ6 x2 = 10 , y2 = โ16 , z2 = 6 Coordinate of A are (a, b, c) = ((10 (1) + 4 (2))/(1 + 2),(โ16 (1) + 2 (2))/(1 + 2),(6 (1) + (โ 6) (2))/(1 + 2)) (a, b, c) = ((10 + 8)/3,(โ 16 + 4)/3,(6 โ 12)/3) (a, b, c) = (6, โ4, โ2) Hence, coordinates of A = (6, โ4, โ2) Now, Point B (p, q, r) divides AQ in the ratio 1 : 1 So, B is mid-point of AQ Coordinates of B = ((๐ฅ_(1 )+ ๐ฅ_2)/2,(๐ฆ_(1 )+ ๐ฆ_2)/2,(๐ง_(1 )+ ๐ง_2)/2) = ((6 + 10)/2,(โ4 + (โ16))/2,(โ2 + 6)/2) = (160/2,(โ20)/2,4/2) = (8, โ10, 2) Hence coordinate of Point B = (8, โ10, 2)