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1
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33

The rate of increase, of a scalar field $$f(x,y,z) = xyz$$, in the direction $$v = (2,1,2)$$ at a point (0,2,1) is

A
$${2 \over 3}$$
B
$${4 \over 3}$$
C
2
D
4
2
GATE ECE 2020
MCQ (Single Correct Answer)
+1
-0.33

For a vector field $\vec{A}$, which one of the following is FALSE?

A

$\vec{A}$ is solenoid if $\nabla \cdot \vec{A}=0$.

B

$\nabla \times(\nabla \times \vec{A})=\nabla(\nabla \cdot \vec{A})-\nabla^2 \vec{A}$

C

$\nabla \times \vec{A}$ is another vector field.

D

$\vec{A}$ is irrotational if $\nabla^2 \vec{A}=0$.

3
GATE ECE 2017 Set 2
Numerical
+1
-0
The smaller angle (in degrees) between the planes $$x+y+z=1$$ and $$2x-y+2z=0$$ is ________.
Your input ____
4
GATE ECE 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
A vector $$\overrightarrow P $$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrightarrow a {}_y - {x^2}yz\overrightarrow a {}_z.\,\,\,$$ Which one of the following statements is TRUE?
A
$$\overrightarrow P $$ is solenoidal, but not irrotational
B
$$\overrightarrow P $$ is irrotational, but not solenoidal
C
$$\overrightarrow P $$ is neither solenoidal nor irrotational
D
$$\overrightarrow P $$ is both solenoidal and irrotational
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