# 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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