# Vector Calculus · Engineering Mathematics · GATE IN

Start Practice## 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...