1
GATE ME 2020 Set 1
Numerical
+1
-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 ____
2
GATE ME 2015 Set 3
MCQ (Single Correct Answer)
+1
-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?
A
$$Curl\left( {\phi \overrightarrow V } \right) = \nabla \left( {\phi Div\overrightarrow V } \right)$$
B
$${Div\overrightarrow V = 0}$$
C
$${Div\,\,Curl\,\,\overrightarrow V = 0}$$
D
$$Div\,\,\left( {\phi \overrightarrow V } \right) = \phi Div\overrightarrow V $$
3
GATE ME 2015 Set 2
MCQ (Single Correct Answer)
+1
-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
A
$$-3i$$
B
$$3i$$
C
$$3i-4j$$
D
$$3i-6k$$
4
GATE ME 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Curl of vector $$\,\,\overrightarrow F = {x^2}{z^2}\widehat i - 2x{y^2}z\widehat j + 2{y^2}{z^3}\widehat k\,\,$$ is
A
$$\left( {4y{z^3} + 2x{y^2}} \right)\widehat i + 2{x^2}z\widehat j - 2{y^2}z\widehat k$$
B
$$\,\left( {4y{z^3} + 2x{y^2}} \right)\widehat i - 2{x^2}z\widehat j - 2{y^2}z\widehat k$$
C
$$2x{z^2}\widehat i - 4xyz\widehat j + 6{y^2}{z^2}\widehat k$$
D
$$2x{z^2}\widehat i + 4xyz\widehat j + 6{y^2}{z^2}\widehat k$$
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