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The vector that is NOT perpendicular to the vectors $$\,\,\left( {i + j + k} \right)\,\,$$ and $$\,\left( {i + 2j + 3k} ... GATE IN 2016 The magnitude of the directional derivative of the function$$f\left( {x,y} \right) = {x^2} + 3{y^2}$$in a direction no... GATE IN 2015$$A$$vector is defined as$$f = y\widehat i + x\widehat j + z\widehat k\,\,$$. Where$$\widehat i,\widehat j,$$and$$...
GATE IN 2014
For a vector $$E,$$ which one of the following statements is NOT TRUE?
GATE IN 2013
A sphere of unit radius is centered at the origin. The unit normal at a point $$(x, y, z)$$ on the surface of the sphere...
GATE IN 2009
If a vector $$\overrightarrow R \left( t \right)$$ has a constant magnitude then
GATE IN 2005

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The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} = ... GATE IN 2012 A scalar field is given by$$f = {x^{2/3}} + {y^{2/3}},$$where$$x$$and$$y are the Cartesian coordinates. The deriv...
GATE IN 2005

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