Find the coordinates of the point where the line (x+3)/3 = (y-1)/(-1) = (z-5)/(-5) cuts the XY Plane.

 

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Note : This is similar to Example 30 of NCERT – Chapter 11 Class 12 Three Dimensional Geometry

Check the answer here https:// www.teachoo.com /3586/756/Example-30---Find-point-where-line-crosses-the-XY-plane/category/Examples/

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 14 Find the coordinates of the point where the line (๐‘ฅ + 3)/3 = (๐‘ฆ โˆ’ 1)/(โˆ’1) = (๐‘ง โˆ’ 5)/(โˆ’5) cuts the XY Plane. If line (๐‘ฅ + 3)/3 = (๐‘ฆ โˆ’ 1)/(โˆ’1) = (๐‘ง โˆ’ 5)/(โˆ’5) cuts the XY Plane Then z = 0 So, let coordinates of point be (x, y, 0) Now, (๐‘ฅ + 3)/3 = (๐‘ฆ โˆ’ 1)/(โˆ’1) = (๐‘ง โˆ’ 5)/(โˆ’5) = k Thus, x = 3k โˆ’ 3, y = โˆ’k + 1, z = โˆ’5k + 5 Since z = 0 โˆ’5k + 5 = 0 5k = 5 k = 5/5 k = 1 Now, x = 3k โˆ’ 3 = 3(1) โˆ’ 3 = 0 y = โˆ’k + 1 = โˆ’1 + 1 = 0 Thus, Coordinates of Point are (0, 0, 0)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.