The three lines whose direction ratios are 2, 3, 6; 3, −6, 2 and 6, 2, −3 are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → mutually perpendicular
Two lines are perpendicular when \(a_1a_2+b_1b_2+c_1c_2 = 0\). Taking the three pairs:
\((2)(3)+(3)(-6)+(6)(2) = 6-18+12 = 0\)
\((3)(6)+(-6)(2)+(2)(-3) = 18-12-6 = 0\)
\((2)(6)+(3)(2)+(6)(-3) = 12+6-18 = 0\)
Every pair is perpendicular, so the lines are mutually perpendicular. This also rules out options (2), (3) and (4).