Project ForgeEngineering Mathematics
Linear Algebra
GATE 2010
Hard
If u⃗=yi+xyj and v⃗=x²i+xy²j, then curl(u⃗×v⃗) is
- A(2xy²)i−(x+y²)j
- B(xy−x²)i−(y−3xy)j
- C(2x²y²−3x³)i−(y³−3xy²)k
- (3xy²−x³)i−(y³−3x²y)j
Explanation
u⃗×v⃗=(0,0,xy³−x³y) (only the z-component is nonzero). curl of a purely-z field F=(0,0,Fz) is (∂Fz/∂y, −∂Fz/∂x, 0)=(3xy²−x³, −(y³−3x²y), 0).
Source: GATE CH 2010 (2010)
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