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

CBSE Class 12 Sample Paper for 2024 Boards
CBSE Class 12 Sample Paper for 2024 Boards
Last updated at Feb. 10, 2025 by Teachoo
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)