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The divergence of the vector field $$\,V = {x^2}i + 2{y^3}j + {z^4}k\,\,$$ at $$x=1, y=2, z=3$$ is ________.
GATE CE 2017 Set 2
For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\o... GATE CE 2012 If$$\overrightarrow a $$and$$\overrightarrow b $$are two arbitrary vectors with magnitudes$$a$$and$$b$$respectiv... GATE CE 2011 For a scalar function$$f(x,y,z)={x^2} + 3{y^2} + 2{z^2},\,\,$$the gradient at the point$$P(1,2,-1)$$is GATE CE 2009 The vector field$$\,F = x\widehat i - y\widehat j\,\,$$(where$$\widehat i$$and$$\widehat j$$are unit vectors) is GATE CE 2003 For the function$$\phi = a{x^2}y - {y^3}$$to represent the velocity potential of an ideal fluid,$${\nabla ^2}\,\,\p...
GATE CE 1999
The directional derivative of the function $$f(x, y, z) = x + y$$ at the point $$P(1,1,0)$$ along the direction $$\over... GATE CE 1996 The derivative of$$f(x, y)$$at point$$(1, 2)$$in the direction of vector$$\overrightarrow i + \overrightarrow j $$... GATE CE 1995 ## Marks 2 More The directional derivative of the field$$u(x, y, z)={x^2} - 3yz$$in the direction of the vector$$\left( {\wideh...
GATE CE 2015 Set 1
A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2... GATE CE 2014 Set 1 For a scalar function$$\,f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 2{z^2},\,\,$$the directional derivative at the poi... GATE CE 2009 The velocity vector is given as$${\mkern 1mu} \vec V = 5xy\widehat i + 2{y^2}\widehat j + 3y{z^2}\widehat k.{\mkern 1mu...
GATE CE 2007
The directional derivative of $$\,\,f\left( {x,y,z} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at the point $$P(2,1,3)$$ ...
GATE CE 2006
The line integral $$\int {\,\,V.dr\,\,}$$ of the vector function $$V\left( r \right) = 2xyz\widehat i + {x^2}z\widehat ... GATE CE 2005 Value of the integral$$\,\,\oint {xydy - {y^2}dx,\,\,} $$where,$$c$$is the square cut from the first quadrant by the... GATE CE 2005 The directional derivative of the following function at$$(1, 2)$$in the direction of$$(4i+3j)$$is :$$f\left( {x,y}...
GATE CE 2002

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