Ex 12.3, 2 - Given that P (3, 2, -4), Q (5, 4, -6) collinear

Ex 12.3,  2 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry - Part 2
Ex 12.3,  2 - Chapter 12 Class 11 Introduction to Three Dimensional Geometry - Part 3

Go Ad-free

Transcript

Question 2 Given that P (3, 2, –4), Q (5, 4, –6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR. Given that Point P (3, 2, –4), Q (5, 4, –6) & R (9, 8, –10) are collinear Q must divide line segment PR in some ratio externally & internally . We know that Co-ordinate of point P(x, y ,z) that divides line segment joining (x1, y1, z1) & (x2, y2, z2) in ration m : n is (x, y ,z) = ((mx2 + nx1)/(m + n),(my2 + ny1)/(m + n), (〖𝑚𝑧〗_2 + 〖𝑛𝑧〗_1)/(𝑚 + 𝑛)) Let point Q (5, 4, –6) divide line segment P (3, 2, – 4), R (9, 8, – 10) in the ratio k : 1 Here, x1 = 3, y1 = 2, z1 = – 4 x2 = 9, y2 = 8, z2 = – 10 & m = k , n = 1 Putting values Q (5, 4, – 6) = ((k(9) + 3)/(k+1),(k(8) + 2)/(k+1),(k(−10) − 4)/(k+1)) (5, 4, – 6) = ((9𝑘 + 3)/(k + 1),(8𝑘 + 2)/(k + 1),(− 10𝑘 −4)/(k+1)) Comparing x – coordinate of Q 5 = (9k + 3)/(k + 1) 5 (k + 1) = 9k + 3 5k + 5 = 9k + 3 5k – 9k = 3 – 5 – 4k = – 2 k = (−2)/(−4) k = 1/2 So, k : 1 = 1 : 2 Thus, point Q divides PR in the Ratio 1 : 2

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.