1
GATE CE 2024 Set 2
MCQ (More than One Correct Answer)
+2
-0.833
Three vectors $\overrightarrow{p}$, $\overrightarrow{q}$, and $\overrightarrow{r}$ are given as
$ \overrightarrow{p} = \hat{i} + \hat{j} + \hat{k}$
$ \overrightarrow{q} = \hat{i} + 2\hat{j} + 3\hat{k}$
$ \overrightarrow{r} = 2\hat{i} + 3\hat{j} + 4\hat{k}$
Which of the following is/are CORRECT?
2
GATE CE 2024 Set 1
MCQ (Single Correct Answer)
+2
-0.833
A vector field $\vec{p}$ and a scalar field $r$ are given by:
$\vec{p} = (2x^2 - 3xy + z^2) \hat{i} + (2y^2 - 3yz + x^2) \hat{j} + (2z^2 - 3xz + x^2) \hat{k}$
$r = 6x^2 + 4y^2 - z^2 - 9xyz - 2xy + 3xz - yz$
Consider the statements P and Q:
P: Curl of the gradient of the scalar field $r$ is a null vector.
Q: Divergence of curl of the vector field $\vec{p}$ is zero.
Which one of the following options is CORRECT?
3
GATE CE 2015 Set 1
Numerical
+2
-0
The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\widehat i + \widehat j - 2\widehat k} \right)\,\,$$ at point $$(2, -1, 4)$$ is _______.
Your input ____
4
GATE CE 2014 Set 1
Numerical
+2
-0
A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$$ $$sin$$ $$(5t),$$ where $$x, y$$ and $$z$$ show variations of the distance covered by the particle (in cm) with time $$t $$ (in $$s$$). The magnitude of the acceleration of the particle (in cm/s2) at $$t=0$$ is _______.
Your input ____
Questions Asked from Vector Calculus (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Levelling Traversing Theodolites and Plane Table Surveying Measurement of Area, Volume and Theory of Errors and Survey Adjustment Field Astronomy and Photogrammetric Surveying Basics of GIS, GPS and Remote Sensing Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey
Engineering Mechanics
Hydrology
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude