Question

If the direction ratios of two mutually perpendicular lines be 3, 5, 7 and a, b, 2 then the value of 3a + 5b is

(A) 16

(B) -16

(C) 14

(D) -14

Answer 1

Correct option is (D) -14

Both lines are perpendicular.

\(\therefore 3a + 5b + 14 = 0\)

⇒ \(3a + 5b = -14\)

Answer 2

Scalor product of 2 mutually perpendicular vector is 0.

i.e \(a_1a_2 + b_1b_2 + c_1c_2 = 0.\)

Given: (3,5,7) and (a,b,2) 

            3*a + 5*b + 7*2 = 0.

            3a + 5b + 14 = 0.

            3a + 5b = -14

Option D : -14.