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

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