GATE ME 2024 | Vector Calculus Question 1 | Engineering Mathematics

GATE ME 2024

MCQ (Single Correct Answer)

-0.33

The value of the surface integral

GATE ME 2024 Engineering Mathematics - Vector Calculus Question 1 English

where S is the external surface of the sphere x² + y² + z² = R² is

$ 4 \pi R^{3} $

$ \frac{4\pi}{3} R^{3} $

$ \pi R^{3} $

GATE ME 2020 Set 1

Numerical

-0

For three vectors $$\vec A = 2\hat j - 3\hat k,\vec B = - 2\hat i + \hat k\ and\;\vec C = 3\hat i - \hat j,$$ where î, ĵ and k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of $$\left( {\vec {A.} \left( {\vec B \times \vec C} \right) + 6} \right)$$ is _______.

Your input ____

GATE ME 2015 Set 3

MCQ (Single Correct Answer)

-0.3

Let $$\phi $$ be an arbitrary smooth real valued scalar function and $$\overrightarrow V $$ be an arbitrary smooth vector valued function in a three dimensional space. Which one of the following is an identity?

$$Curl\left( {\phi \overrightarrow V } \right) = \nabla \left( {\phi Div\overrightarrow V } \right)$$

$${Div\overrightarrow V = 0}$$

$${Div\,\,Curl\,\,\overrightarrow V = 0}$$

$$Div\,\,\left( {\phi \overrightarrow V } \right) = \phi Div\overrightarrow V $$

GATE ME 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is

$$-3i$$

$$3i$$

$$3i-4j$$

$$3i-6k$$