# Vector Calculus · Engineering Mathematics · GATE IN

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## Marks 1

GATE IN 2016
The vector that is NOT perpendicular to the vectors $$\,\,\left( {i + j + k} \right)\,\,$$ and $$\,\left( {i + 2j + 3k} \right)\,\,$$ is _________.
GATE IN 2015
The magnitude of the directional derivative of the function $$f\left( {x,y} \right) = {x^2} + 3{y^2}$$ in a direction normal to the circle $$\,{x^2} +... GATE IN 2014$$A$$vector is defined as$$f = y\widehat i + x\widehat j + z\widehat k\,\,$$. Where$$\widehat i,\widehat j,$$and$$\widehat k$$are unit vectors ... GATE IN 2013 For a vector$$E,$$which one of the following statements is NOT TRUE? GATE IN 2009 A sphere of unit radius is centered at the origin. The unit normal at a point$$(x, y, z)$$on the surface of the sphere is the vector. GATE IN 2005 If a vector$$\overrightarrow R \left( t \right)$$has a constant magnitude then ## Marks 2 GATE IN 2012 The direction of vector$$A$$is radially outward from the origin, with$$\left| A \right| = K\,{r^n}$$where$${r^2} = {x^2} + {y^2} + {z^2}$$and ... GATE IN 2005 A scalar field is given by$$f = {x^{2/3}} + {y^{2/3}},$$where$$x$$and$$y$$are the Cartesian coordinates. The derivative of$$'f' along the lin...
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