Last updated at May 29, 2018 by Teachoo

Transcript

Misc 12 Find the coordinates of the point where the line through (3, 4, 5) and (2, 3, 1) crosses the plane 2x + y + z = 7. The equation of a line passing through two points A( 1 , 1 , 1 ) and B( 2 , 2 , 2 ) is = = Given the line passes through the points So, the equation of line is 3 2 3 = ( 4) 3 ( 4) = ( 5) 1 ( 5) = + = + = k So, Let (x, y, z) be the coordinates of the point where the line crosses the plane 2x + y + z = 7 Putting value of x, y, z, from (1) in the equation of plane, 2x + y + z = 7 2( k + 3) + (k 4) + (6k 5) = 7 2k + 6 + k 4 + 6k 5 = 7 5k 3 = 7 5k = 7 + 3 5k = 10 k = = 2 Putting value of k in x, y, z, x = k + 3 = 2 + 3 = 1 y = k 4 = 2 4 = 2 z = 6k 5 = 6 2 5 = 12 5 = 7 Therefore, the coordinate of the required point are (1, 2, 7).

Chapter 11 Class 12 Three Dimensional Geometry

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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.