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GATE ECE

Vector Calculus

Engineering Mathematics

Previous Years Questions

Marks 1

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The smaller angle (in degrees) between the planes $$x+y+z=1$$ and $$2x-y+2z=0$$ is ________.
GATE ECE 2017 Set 2
A vector $$\overrightarrow P $$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrig...
GATE ECE 2015 Set 1
If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarr...
GATE ECE 2014 Set 2
The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$ ...
GATE ECE 2014 Set 4
The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(...
GATE ECE 2014 Set 4
Consider a vector field $$\overrightarrow A \left( {\overrightarrow r } \right).$$ The closed loop line integral $$\oint...
GATE ECE 2013
Consider a closed surface $$'S'$$ surrounding a volume $$V.$$ If $$\overrightarrow r $$ is the position vector of a poin...
GATE ECE 2011
$$\nabla \times \left( {\nabla \times P} \right)\,\,$$ where $$P$$ is a vector is equal to
GATE ECE 2005
If the linear velocity $${\overrightarrow V }$$ is given by $$\overrightarrow V = {x^2}y\overrightarrow i + xyz\overri...
GATE ECE 1993

Marks 2

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Let $$\,\,\,{\rm I} = \int_c {\left( {2z\,dx + 2y\,dy + 2x\,dz} \right)} \,\,\,\,$$ where $$x, y, z$$ are real, and let...
GATE ECE 2017 Set 1
If the vector function $$\,\,\overrightarrow F = \widehat a{}_x\left( {3y - k{}_1z} \right) + \widehat a{}_y\left( {k{...
GATE ECE 2017 Set 1
Suppose $$C$$ is the closed curve defined as the circle $$\,\,{x^2} + {y^2} = 1\,\,$$ with $$C$$ oriented anti-clockwis...
GATE ECE 2016 Set 2
Given $$\,\,\overrightarrow F = z\widehat a{}_x + x\widehat a{}_y + y\widehat a{}_z.\,\,$$ If $$S$$ represents the po...
GATE ECE 2014 Set 4
The divergence of the vector field $$\,\overrightarrow A = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,$$ ...
GATE ECE 2013
The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} ...
GATE ECE 2012
If $$\overrightarrow A = xy\,\widehat a{}_x + {x^2}\widehat a{}_y\,\,$$ then $$\,\,\oint {\overrightarrow A .d\overrigh...
GATE ECE 2010
If a vector field$$\overrightarrow V $$ is related to another field $$\overrightarrow A $$ through $$\,\overrightarrow ...
GATE ECE 2009
Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q...
GATE ECE 2008

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