Project ForgeEngineering Mathematics
Linear Algebra
GATE 2020
Medium
Consider the continuously differentiable function v(x,y,z)=3x²y i+8y²z j+5xyz k, where i,j,k are the unit vectors along x,y,z. The curl of this function is
- A−3x² i − 8y² j + 5z(x+y) k
- B6xy i − 16yz j + 5xy k
- (5xz−8y²) i − 5yz j − 3x² k
- Dy(11x+16z)
Explanation
curl F=(∂Fz/∂y−∂Fy/∂z, ∂Fx/∂z−∂Fz/∂x, ∂Fy/∂x−∂Fx/∂y). With Fx=3x²y, Fy=8y²z, Fz=5xyz: i-component=5xz−8y², j-component=0−5yz=−5yz, k-component=0−3x²=−3x². So curl=(5xz−8y²)i−5yz j−3x²k.
Source: GATE CH 2020 (2020)
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