For A⃗ = 2î + aĵ + k̂ and B⃗ = 4î − 2ĵ − 2k̂, find a such that A⃗ is perpendicular to B⃗.
Physics · Mixed Chapter
JEE Main Practice

Question

For A⃗ = 2î + aĵ + k̂ and B⃗ = 4î − 2ĵ − 2k̂, find a such that A⃗ is perpendicular to B⃗.

G1 Physics · Accepted Answer

Step 1: Orthogonality requires A⃗·B⃗ = 0. Step 2: Dot product = (2)(4) + a(−2) + (1)(−2) = 8−2a−2 = 6−2a. Step 3: 6−2a = 0 gives a = 3.