A drone at a Diwali festival flies along the vector r = 2i + j + k + μ(i + j). What is its shortest distance from a static firework rocket launched vertically along the z-axis (r = λk)?

A drone at a Diwali festival flies along the vector r = 2i + j + k + μ(i + j). What is its shortest distance from a static firework rocket launched vertically along the z-axis (r = λk)?

• A. 1/√2 units
• B. 1 unit
• C. √2 units
• D. 0 units

Answer: A) 1/√2 units

Explanation: Line 1: a₁ = 2i + j + k, b₁ = i + j. Line 2: a₂ = 0, b₂ = k. Shortest distance = |(a₂ − a₁) · (b₁ × b₂)| / |b₁ × b₂|. a₂ − a₁ = −2i − j − k. b₁ × b₂ = (i+j) × k = −j + i = i − j. (a₂ − a₁) · (b₁ × b₂) = (−2)(1) + (−1)(−1) + 0 = −2 + 1 = −1. |b₁ × b₂| = √2. SD = |−1| / √2 = 1/√2.