Question 1 (i) - Section - Defination - Chapter 11 Class 11 - Intro to Three Dimensional Geometry

Last updated at April 16, 2024 by Teachoo

Transcript

Example 7
Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) in the ratio 2 : 3
(i) internally,
Let the 2 given points be
A (1, −2, 3)
& B (3, 4, –5)
Let P (x, y, z,) be points that divides line in ratio 2:3 internally
We know that
Co-ordinate of point P (x, y, z) 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, x1 = 1, y1 = – 2, z1 = 3
x2 = 3, y2 = 4, z2 = – 5
& m = 2, n = 3
Putting values
Co-ordinate of point P of
(x, y, z) = ((2(3) + 3(1))/(2 + 3),(2(4) + 3(−2))/(2 + 3),(2(−5) + 3(3))/(2 + 3))
= ((6 + 3)/5,(8 − 6)/5,(−10 + 9)/5)
= (9/5,2/5,(−1)/5)
Thus, the required co-ordinate is (𝟗/𝟓,𝟐/𝟓,(−𝟏)/𝟓)

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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