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Last updated at Feb. 1, 2020 by Teachoo
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Ex 11.2, 7 The Cartesian equation of a line is (๐ฅ โ 5)/3 = (๐ฆ + 4)/7 = (๐ง โ 6)/2. Write its vector form.Cartesian equation : (๐ฅ โ 5)/3 = (๐ฆ + 4)/7 = (๐ง โ 6)/2 (๐ฅ โ 5)/3 = (๐ฆ โ (โ4))/7 = (๐ง โ 6)/2 Equation of a line in Cartesian form is given by (๐ฅ โ ๐ฅ1)/๐ = (๐ฆ โ ๐ฆ1)/๐ = (๐ง โ ๐ง1)/๐ Comparing (1) and (2), ๐ฅ1 = 5, ๐ฆ1 = โ4, ๐ง1 = 6 ๐ = 3, b = 7, c = 2 Cartesian equation : (๐ฅ โ 5)/3 = (๐ฆ + 4)/7 = (๐ง โ 6)/2 (๐ฅ โ 5)/3 = (๐ฆ โ (โ4))/7 = (๐ง โ 6)/2 Equation of a line in Cartesian form is given by (๐ฅ โ ๐ฅ1)/๐ = (๐ฆ โ ๐ฆ1)/๐ = (๐ง โ ๐ง1)/๐ Comparing (1) and (2), ๐ฅ1 = 5, ๐ฆ1 = โ4, ๐ง1 = 6 ๐ = 3, b = 7, c = 2 Equation of line in vector form is ๐ โ = ๐ โ + ๐๐ โ Where ๐ โ = ๐ฅ1๐ ฬ + y1๐ ฬ + z1๐ ฬ = 5๐ ฬ โ 4๐ ฬ + 6๐ ฬ & ๐ โ = ๐๐ ฬ + b๐ ฬ + c๐ ฬ = 3๐ ฬ + 7๐ ฬ + 2๐ ฬ Now, ๐ โ = (5๐ ฬ โ 4๐ ฬ + 6๐ ฬ) + ๐ (3๐ ฬ + 7๐ ฬ + 2๐ ฬ)
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