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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 ⃗ + 𝜆𝒃 ⃗ Where 𝒂 ⃗ = 𝑥1𝑖 ̂ + y1𝑗 ̂ + z1𝑘 ̂ = 5𝒊 ̂ − 4𝒋 ̂ + 6𝒌 ̂ & 𝒃 ⃗ = 𝑎𝑖 ̂ + b𝑗 ̂ + c𝑘 ̂ = 3𝒊 ̂ + 7𝒋 ̂ + 2𝒌 ̂ Now, 𝑟 ⃗ = (5𝒊 ̂ − 4𝒋 ̂ + 6𝒌 ̂) + 𝜆 (3𝒊 ̂ + 7𝒋 ̂ + 2𝒌 ̂)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo