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, –4, –5) and (2, –3, 1) crosses the plane 2x + y + z = 7. The equation of a line passing through two points A( 𝑥﷮1﷯, 𝑦﷮1﷯, 𝑧﷮1﷯) and B( 𝑥﷮2﷯, 𝑦﷮2﷯, 𝑧﷮2﷯) is 𝒙 − 𝒙﷮𝟏﷯﷮ 𝒙﷮𝟐﷯ − 𝒙﷮𝟏﷯﷯ = 𝒚 − 𝒚﷮𝟏﷯﷮ 𝒚﷮𝟐﷯ − 𝒚﷮𝟏﷯﷯ = 𝒛 − 𝒛﷮𝟏﷯﷮ 𝒛﷮𝟐﷯ − 𝒛﷮𝟏﷯﷯ Given the line passes through the points So, the equation of line is 𝑥 − 3﷮2 − 3﷯ = 𝑦 −(−4)﷮−3 −(−4)﷯ = 𝑧 −(−5)﷮1 −(−5)﷯ 𝒙 − 𝟑﷮−𝟏﷯ = 𝒚 + 𝟒﷮𝟏﷯ = 𝒛 + 𝟓﷮𝟔﷯ = 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 = 𝟏𝟎﷮𝟓﷯ = 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).