Ex 11.2, 6

Transcript

Ex 11.2, 6 Find the Cartesian equation of the line which passes through the point (– 2, 4, – 5) and parallel to the line given by 𝑥 + 3﷮3﷯ = 𝑦 − 4﷮5﷯ = 𝑧 + 8﷮6﷯. Equation of a line passing through (x1, y1, z1) and parallel to a line having direction ratios a, b, c is 𝑥 − 𝑥1﷮𝑎﷯ = 𝑦 − 𝑦1﷮𝑏﷯ = 𝑧 − 𝑧1﷮𝑐﷯ Since the line passes through (−2, 4, −5) 𝑥1 = −2, y1 = 4 , z1 = −5 Since the line is parallel to 𝑥 + 3﷮3﷯ = 𝑦 − 4﷮5﷯ = 𝑧 + 8﷮6﷯ 𝑎 = 3, b = 5 c = 6 Therefore, equation of line in Cartesian form is 𝑥 − (−2)﷮3﷯ = 𝑦 − 4﷮5﷯ = 𝑧 − (−5)﷮6﷯ 𝒙 + 𝟐﷮𝟑﷯ = 𝒚 − 𝟒﷮𝟓﷯ = 𝒛 + 𝟓﷮𝟔﷯