CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
Last updated at August 14, 2026 by Teachoo
Transcript
Question 10 The equation of the line in vector form passing through the point (−1, 3, 5) and parallel to line (𝑥 − 3)/2 = (𝑦 − 4)/3, z = 2. is (a) 𝑟 ⃗ = (−𝑖 ̂ + 3𝑗 ̂ + 5𝑘 ̂) + 𝜆 (2𝑖 ̂ + 3𝑗 ̂ + 𝑘 ̂) (b) 𝑟 ⃗ = (−𝑖 ̂ + 3𝑗 ̂ + 5𝑘 ̂) + 𝜆 (2𝑖 ̂ + 3𝑗 ̂) (c) 𝑟 ⃗ = (2𝑖 ̂ + 3𝑗 ̂ − 2𝑘 ̂) + 𝜆 (−𝑖 ̂ + 3𝑗 ̂ + 5𝑘 ̂) (d) 𝑟 ⃗ = (2𝑖 ̂ + 3𝑗 ̂) + 𝜆 (−𝑖 ̂ + 3𝑗 ̂ + 5𝑘 ̂) Equation of a line passing through a point with position vector 𝑎 ⃗ and parallel to vector 𝑏 ⃗ is 𝑟 ⃗ = 𝑎 ⃗ + 𝜆𝑏 ⃗ Here, Point is (–1, 3, 5) So, 𝑎 ⃗ = –𝑖 ̂ + 3𝑗 ̂ + 5𝑘 ̂ And it is parallel to line (𝑥 − 3)/2 = (𝑦 − 4)/3, z = 2 This means that z-component of equation is 0 So, line is (𝑥 − 3)/2 = (𝑦 − 4)/3 = (𝑧 − 2)/0 So, 𝑏 ⃗ = 2𝑖 ̂ + 3𝑗 ̂ + 0𝑘 ̂ = 2𝑖 ̂ + 3𝑗 ̂ Thus, Equation of line is 𝒓 ⃗ = (−𝒊 ̂ + 3𝒋 ̂ + 5𝒌 ̂) + 𝝀 (2𝒊 ̂ + 3𝒋 ̂) So, (b) is the correct answer
