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Last updated at Feb. 1, 2020 by Teachoo

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Misc 12 Find the coordinates of the point where the line through (3, โ4, โ5) and (2, โ3, 1) crosses the plane 2x + y + z = 7. The equation of a line passing through two points A(๐ฅ_1, ๐ฆ_1, ๐ง_1) and B(๐ฅ_2, ๐ฆ_2, ๐ง_2) is (๐ โ ๐_๐)/(๐_๐ โ ๐_๐ ) = (๐ โ ๐_๐)/(๐_๐ โ ๐_๐ ) = (๐ โ ๐_๐)/(๐_๐ โ ๐_๐ ) Given the line passes through the points A (3, โ4, โ5) โด๐ฅ_1 = 3, ๐ฆ_1= โ4, ๐ง_1= โ5 B (2, โ3, 1) โด๐ฅ_2 = 2, ๐ฆ_2= โ3, ๐ง_2= 1 So, the equation of line is (๐ฅ โ 3)/(2 โ 3) = (๐ฆ โ (โ4))/(โ3 โ (โ4)) = (๐ง โ (โ5))/(1 โ (โ5)) (๐ โ ๐)/(โ๐) = (๐ + ๐)/๐ = (๐ + ๐)/๐ = 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 x = โk + 3 2(โk + 3) + (k โ 4) + (6k โ 5) = 7 โ2k + 6 + k โ 4 + 6k โ 5 = 7 5k โ 3 = 7 5k = 7 + 3 5k = 10 โด k = ๐๐/๐ = 2 Putting value of k in x, y, z, x = โk + 3 = โ2 + 3 = 1 y = k โ 4 = 2 โ 4 = โ2 z = 6k โ 5 = 6 ร 2 โ 5 = 12 โ 5 = 7 Therefore, the coordinate of the required point are (1, โ2, 7).

Miscellaneous

Misc 1
Important

Misc 2

Misc 3 Deleted for CBSE Board 2021 Exams only

Misc 4 Important

Misc 5 Important Deleted for CBSE Board 2021 Exams only

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important You are here

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21 Important

Misc 22 Important

Misc 23 Important

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.