Answer :

Solution :

Given, scalar point function,

ƒ(x,y,z) = 4x²+7xy+3xz²

Gradient gives the direction in which the directional derivative will be maximum

Grad(ƒ)=∇.ƒ

∇.ƒ= (î∂/∂x+Ĵ∂/∂y+ k̂∂/∂z)(4x2+7xy+3xz2)

∇.ƒ=(8x+7y+3z2)î+(7x)Ĵ+(6xz) k̂

At point, P(1,0,2),

∇.ƒ=(8×1+7×0+3×2²)î+(7×1)Ĵ+(6×1×2) k̂

∇.ƒ=20î+ 7Ĵ + 12k̂

Hence, the correct option is (B).