1
GATE IN 2016
MCQ (Single Correct Answer)
+1
-0.3
The vector that is NOT perpendicular to the vectors $$\,\,\left( {i + j + k} \right)\,\,$$ and $$\,\left( {i + 2j + 3k} \right)\,\,$$ is _________.
A
$$\,\left( {i - 2j + k} \right)\,\,$$
B
$$\,\left( {-i + 2j - k} \right)\,\,$$
C
$$\,\left( {0i + 0j + 0k} \right)\,\,$$
D
$$\,\left( {4i + 3j + 5k} \right)\,\,$$
2
GATE IN 2015
MCQ (Single Correct Answer)
+1
-0.3
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 $$\,{x^2} + {y^2} = 2,$$ at the point $$(1,1),$$ is
A
$$4\sqrt 2 $$
B
$$5\sqrt 2 $$
C
$$7\sqrt 2 $$
D
$$9\sqrt 2 $$
3
GATE IN 2014
Numerical
+1
-0
$$A$$ 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 in cartesian $$(x, y, z)$$ coordinate system. The surface integral - GATE IN 2014 Engineering Mathematics - Vector Calculus Question 3 English -over the closed surface $$S$$ of a cube with vertices having the following coordinates: $$(0,0,0), (1, 0, 0), (0, 1, 0), (0,0,1), (1, 0, 1), (1,1,1), (0, 1, 1), (1, 1, 0)$$ is _______.
Your input ____
4
GATE IN 2013
MCQ (Single Correct Answer)
+1
-0.3
For a vector $$E,$$ which one of the following statements is NOT TRUE?
A
If $$\nabla .E = 0,E$$ is called
B
If $$\nabla \times E = 0,$$ $$E$$ is called conservative
C
If $$\nabla \times E = 0,$$ $$E$$ is called irrotational
D
If $$\nabla .E = 0,E$$ is called irrotational
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