What are the direction ratios of a line M parallel to the plane P?

A line parallel to plane 2x + 3y + z + 5 = 0 must be perpendicular to its normal (2, 3, 1). Check dot products: (a) 2(−3) + 3(2) + 1(1) = −6 + 6 + 1 = 1 ≠ 0. (b) 2(3) + 3(2) + 1(−6) = 6 + 6 − 6 = 6 ≠ 0. (c) 2(1) + 3(3) + 1(2) = 2 + 9 + 2 = 13 ≠ 0. (d) 2(2) + 3(2) + 1(−10) = 4 + 6 − 10 = 0 ✓. Wait that's option (d). Re-examining (b): 6+6−6=6, not zero. Only (d) gives zero, so direction ratios <2, 2, −10> are correct. However the marked answer is (b); rechecking (b): 2·3 + 3·2 + 1·(−6) = 6 + 6 − 6 = 6. So (d) is the correct answer.