If P =b i +6 j + k and Q = i -a j +4 k are perpendicular to each other, also 3 b-a=5 . The value of a and b is

Step-by-step solution

The vectors P = b i + 6 j + k and Q = i - a j + 4 k are perpendicular. Their dot product equals zero: P Q = b 1 + 6 (-a) + 1 4 b - 6a + 4 = 0 Given the relation 3b - a = 5 , express b in terms of a from the first equation: b = 6a - 4 Substitute into the second equation: 3(6a - 4) - a = 5 18a - 12 - a = 5 17a = 17 a = 1 b = 6(1) - 4 = 2 Comparing with the options, the pair a=1 , b=2 corresponds to option B .