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ISRO Scientist Electrical 2019 Paper

Option 1 : 1

Given that,

ϕ = xy^{2} + yz^{2} + zx^{2}

directional vector (p) = I + 2j + 2K

Directional derivative \( = \nabla \phi .\hat P = \nabla \phi .\frac{{\vec P}}{{\left| {\vec P} \right|}}\)

\(\nabla \phi = \frac{{\partial \phi }}{{\partial x}}\hat i + \frac{{\partial \phi }}{{\partial y}}\hat i + \frac{{\partial \phi }}{{\partial z}} \hat k\)

= (y^{2} + 2xz) î + (2xy + z^{2}) ĵ + (2yz + x^{2}) k̂

∇ϕ at the point (2, -1, 1) is

∇ϕ = ((-1)^{2} + 2(2)(1)) î + (2(2)(-1) + (1)^{2}) ĵ + (2(-1)(1) + (2)^{2})k̂

= 5î - 3ĵ + 2k̂

Directional derivative = \(\left( {5i - 3j + 2k} \right).\frac{{i + 2j + 2k}}{{\sqrt {{1^2} + {2^2} + {2^2}} }}\)

\(= \frac{{5 - 6 + 4}}{3} = 1\)

CT 1: Ratio and Proportion

3941

10 Questions
16 Marks
30 Mins