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.
Let A be (–2, 3, 5)
& B be (1, –4, 6)
Let coordinate of point P be (x, y, z) that divides the line joining A & B in the ratio of 2 : 3 internally
We know that
Coordinate of P that divide 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, x1 = – 2, y1 = 3, z1 = 5
x2 = 1, y2 = – 4, z2 = 6
& m = 2 , n = 3
Putting values
(x, y, z) = ((2(1) + 3(−2))/(2+3),(2 (−4) + 3(3))/(2+ 3),(2(6) + 3(5))/(2+ 3))
= ((2 − 6)/5,(− 8 + 9)/5,(12 + 15)/( 5))
= ((−4)/( 5),1/5,27/( 5))
Thus, the required coordinate of point P is ((−𝟒)/( 𝟓),𝟏/𝟓,𝟐𝟕/( 𝟓))

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.

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