Ex 11.2, 6 - Chapter 11 Class 12 Three Dimensional Geometry

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