Find the value of λ such that the line (x−2)/3 = (y−1)/λ = (z−3)/2 is parallel to the plane 2x + y − z = 5.

Find the value of λ such that the line (x−2)/3 = (y−1)/λ = (z−3)/2 is parallel to the plane 2x + y − z = 5.

• A. −4
• B. 4
• C. −2
• D. 2

Answer: A) −4

Explanation: If a line is parallel to a plane, it is perpendicular to the normal. So, a(l) + b(m) + c(n) = 0. 2(3) + 1(λ) − 1(2) = 0 → 6 + λ − 2 = 0 → λ = −4.