The lines r =iˆ+jˆ-kˆ+λ(2iˆ+3jˆ-6kˆ) and r =2iˆ-jˆ-kˆ+μ(6iˆ+9jˆ-18kˆ);( where λ &  μ are scalars) are

  (a)coincident              (b) skew          

  (c) intersecting           (d) parallel

[Class 12 - Sample Paper] The lines r = i + j + k - λ(2i+3j-6k) and - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 5 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

 

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Transcript

The given lines are : 𝑟 ⃗=𝑖 ˆ+𝑗 ˆ−𝑘 ˆ+𝜆(𝟐𝒊 ˆ+𝟑𝒋 ˆ−𝟔𝒌 ˆ ) and 𝑟 ⃗=2𝑖 ˆ−𝑗 ˆ−𝑘 ˆ+𝜇(6𝑖 ˆ+9𝑗 ˆ−18𝑘 ˆ) or 𝑟 ⃗=2𝑖 ˆ−𝑗 ˆ−𝑘 ˆ+3𝜇(2𝑖 ˆ+3𝑗 ˆ−6𝑘 ˆ) Let 3𝜇=𝑎 𝑤ℎ𝑒𝑟𝑒 𝑎 𝑖𝑠 𝑎𝑛𝑦 𝑠𝑐𝑎𝑙𝑎𝑟 or 𝑟 ⃗=2𝑖 ˆ−𝑗 ˆ−𝑘 ˆ+𝑎(𝟐𝒊 ˆ+𝟑𝒋 ˆ−𝟔𝒌 ˆ) Since the parallel vector in both is the same Hence, the given lines are parallel So, the correct answer is (d)

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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 15 years. He provides courses for Maths, Science and Computer Science at Teachoo