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Ex 11.2, 7 - Cartesian equation is  x-5/3 = y+4/7 = z-6/2 - Equation of line  - given point and //vector

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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Ex 11.2, 7 The Cartesian equation of a line is 𝑥 − 5﷮3﷯ = 𝑦 + 4﷮7﷯ = 𝑧 − 6﷮2﷯ . Write its vector form. Cartesian equation : 𝑥 − 5﷮3﷯ = 𝑦 + 4﷮7﷯ = 𝑧 − 6﷮2﷯ 𝑥 − 5﷮3﷯ = 𝑦 − (−4)﷮7﷯ = 𝑧 − 6﷮2﷯ Equation of a line in Cartesian form is given by 𝑥 − 𝑥1﷮𝑎﷯ = 𝑦 − 𝑦1﷮𝑏﷯ = 𝑧 − 𝑧1﷮𝑐﷯ Comparing (1) and (2), 𝑥1 = 5, 𝑦1 = −4 𝑧1 = 6 & 𝑎 = 3 , b = 7 c = 2 Equation of line in vector form is 𝑟﷯ = 𝑎﷯ + 𝜆 𝑏﷯ Where 𝑎﷯ = 𝑥1 𝑖﷯ + y1 𝑗﷯ + z1 𝑘﷯ = 5 𝑖﷯ − 4 𝑗﷯ + 6 𝑘﷯ & 𝑏﷯ = 𝑎 𝑖﷯ + b 𝑗﷯ + c 𝑘﷯ = 3 𝑖﷯ + 7 𝑗﷯ + 2 𝑘﷯ Now, 𝑟﷯ = (5 𝒊﷯ − 4 𝒋﷯ + 6 𝒌﷯) + 𝜆 (3 𝒊﷯ + 7 𝒋﷯ + 2 𝒌﷯) Therefore, equation of line in vector form is 𝑟﷯ = (5 𝑖﷯ − 4 𝑗﷯ + 6 𝑘﷯) + 𝜆 (3 𝑖﷯ + 7 𝑗﷯ + 2 𝑘﷯)

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