Slide37.JPG

Slide38.JPG
Slide39.JPG

Subscribe to our Youtube Channel - https://you.tube/teachoo

  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise

Transcript

Misc 12 Find the coordinates of the point where the line through (3, โ€“4, โ€“5) and (2, โ€“3, 1) crosses the plane 2x + y + z = 7. The equation of a line passing through two points A(๐‘ฅ_1, ๐‘ฆ_1, ๐‘ง_1) and B(๐‘ฅ_2, ๐‘ฆ_2, ๐‘ง_2) is (๐’™ โˆ’ ๐’™_๐Ÿ)/(๐’™_๐Ÿ โˆ’ ๐’™_๐Ÿ ) = (๐’š โˆ’ ๐’š_๐Ÿ)/(๐’š_๐Ÿ โˆ’ ๐’š_๐Ÿ ) = (๐’› โˆ’ ๐’›_๐Ÿ)/(๐’›_๐Ÿ โˆ’ ๐’›_๐Ÿ ) Given the line passes through the points A (3, โˆ’4, โˆ’5) โˆด๐‘ฅ_1 = 3, ๐‘ฆ_1= โˆ’4, ๐‘ง_1= โˆ’5 B (2, โˆ’3, 1) โˆด๐‘ฅ_2 = 2, ๐‘ฆ_2= โˆ’3, ๐‘ง_2= 1 So, the equation of line is (๐‘ฅ โˆ’ 3)/(2 โˆ’ 3) = (๐‘ฆ โˆ’ (โˆ’4))/(โˆ’3 โˆ’ (โˆ’4)) = (๐‘ง โˆ’ (โˆ’5))/(1 โˆ’ (โˆ’5)) (๐’™ โˆ’ ๐Ÿ‘)/(โˆ’๐Ÿ) = (๐’š + ๐Ÿ’)/๐Ÿ = (๐’› + ๐Ÿ“)/๐Ÿ” = 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 = โˆ’k + 3 2(โˆ’k + 3) + (k โˆ’ 4) + (6k โˆ’ 5) = 7 โˆ’2k + 6 + k โˆ’ 4 + 6k โˆ’ 5 = 7 5k โˆ’ 3 = 7 5k = 7 + 3 5k = 10 โˆด k = ๐Ÿ๐ŸŽ/๐Ÿ“ = 2 Putting value of k in x, y, z, x = โˆ’k + 3 = โˆ’2 + 3 = 1 y = k โˆ’ 4 = 2 โˆ’ 4 = โˆ’2 z = 6k โˆ’ 5 = 6 ร— 2 โˆ’ 5 = 12 โˆ’ 5 = 7 Therefore, the coordinate of the required point are (1, โˆ’2, 7).

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.