Vectors aî + bĵ + k̂ and 2î - 3ĵ + 4k̂ are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x i s _______ .
Physics · Mathematical tools and vector
JEE Mains 24 January 2023 Shift 1 Morning Shift

Question

Vectors aî + bĵ + k̂ and 2î - 3ĵ + 4k̂ are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x i s _______ .

G1 Physics · Accepted Answer

Perpendicular vectors have zero dot product: 2a - 3b + 4 = 0, so 2a - 3b = -4. Together with 3a + 2b = 7, this gives a = 1 and b = 2. Thus a/b = 1/2 = x/2, so x = 1.