Vector Calculus · Engineering Mathematics · GATE PI

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Marks 1

GATE PI 2014
Directional derivative of $$\phi = 2xz - {y^2}$$ at the point $$(1, 3, 2)$$ becomes maximum in the direction of
GATE PI 2012
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt ...
GATE PI 2011
If $$A$$ $$(0,4,3),$$ $$B(0,0,0)$$ and $$C(3,0,4)$$ are there points defined in $$x, y, z$$ coordinate system, then which one of the following vectors...
GATE PI 2009
The line integral of the vector function $$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$ along the $$x$$ - axis from $$x=1$$ to $$x=2$$ is...
GATE PI 2008
If $$\overrightarrow r $$ is the position vector of any point on a closed surface $$S$$ that encloses the volume $$V$$ then $$\,\,\int {\int\limits_...
GATE PI 2005
Which one of the following is Not associated with vector calculus?

Marks 2

GATE PI 2014
If $$\,\phi = 2{x^3}{y^2}{z^4}$$ then $${\nabla ^2}\phi $$ is
GATE PI 2011
The line integral $$\int\limits_{{P_1}}^{{P_2}} {\left( {ydx + xdy} \right)} $$ from $${P_1}\left( {{x_1},{y_1}} \right)$$ to $${P_2}\left( {{x_2},{y_...
GATE PI 2011
If $$T(x, y, z)$$ $$ = {x^2} + {y^2} + 2{z^2}$$ defines the temperature at any location $$(x, y, z)$$ then the magnitude of the temperature gradient ...
GATE PI 2007
The angle (in degrees) between two planar vectors $$\vec a = {{\sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ and $$\vec b = {{ - \sqrt 3 } ...
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