Last updated at Feb. 1, 2020 by Teachoo
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Example 6 Find the vector and the Cartesian equations of the line through the point (5, 2, โ 4) and which is parallel to the vector 3๐ ฬ + 2๐ ฬ โ 8๐ ฬ . Vector equation Equation of a line passing through a point with position vector ๐ โ , and parallel to a vector ๐ โ is ๐ โ = ๐ โ + ๐๐ โ Since line passes through (5, 2, โ4) ๐ โ = 5๐ ฬ + 2๐ ฬ โ 4๐ ฬ Since line is parallel to 3๐ ฬ + 2๐ ฬ โ 8๐ ฬ ๐ โ = 3๐ ฬ + 2๐ ฬ โ 8๐ ฬ Equation of line ๐ โ = ๐ โ + ๐๐ โ ๐ โ = (5๐ ฬ + 2๐ ฬ โ 4๐ ฬ) + ๐ (3๐ ฬ + 2๐ ฬ โ 8๐ ฬ) Therefore, equation of line in vector form is ๐ โ = (5๐ ฬ + 2๐ ฬ โ 4๐ ฬ) + ๐ (3๐ ฬ + 2๐ ฬ โ 8๐ ฬ) Cartesian equation Equation of a line passing through a point (x, y, z) and parallel to a line with direction ratios a, b, c is (๐ฅ โ ๐ฅ1)/๐ = (๐ฆ โ ๐ฆ1)/๐ = (๐ง โ ๐ง1)/๐ Since line passes through (5, 2, โ4) ๐ฅ1 = 5, y1 = 2 , z1 = โ4 .....................................
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