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## Marks 1

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Directional derivative of $$\phi = 2xz - {y^2}$$ at the point $$(1, 3, 2)$$ becomes maximum in the direction of
GATE PI 2014
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \ove... GATE PI 2012 If$$A(0,4,3),B(0,0,0)$$and$$C(3,0,4)$$are there points defined in$$x, y, z$$coordinate system, then whic... GATE PI 2011 The line integral of the vector function$$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$along the$$x$$- a... GATE PI 2009 If$$\overrightarrow r $$is the position vector of any point on a closed surface$$S$$that encloses the volume$$V$$... GATE PI 2008 Which one of the following is Not associated with vector calculus? GATE PI 2005 ## Marks 2 More If$$\,\phi = 2{x^3}{y^2}{z^4}$$then$${\nabla ^2}\phi $$is GATE PI 2014 If$$T(x, y, z) = {x^2} + {y^2} + 2{z^2}$$defines the temperature at any location$$(x, y, z)$$then the magnitud... GATE PI 2011 The line integral$$\int\limits_{{P_1}}^{{P_2}} {\left( {ydx + xdy} \right)} $$from$${P_1}\left( {{x_1},{y_1}} \right)...
GATE PI 2011
The angle (in degrees) between two planar vectors $$\vec a = {{\sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ a...
GATE PI 2007

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