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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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Find coordinates of point where the line cuts x+3/3 = y-1/-1 XY Plane

Question 14 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

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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/

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Transcript

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

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