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Recent questions tagged vector-identities
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GATE2020-ME-2: 26
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is $3\hat{i} – 3 \hat{j} - \hat{k} \\$ $- \dfrac{7}{3} \\$ $\dfrac{7}{3} \\ $ $7$
go_editor
asked
in
Calculus
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
calculus
vector-identities
directional-derivatives
0
answers
0
votes
GATE2020-ME-1: 27
A vector field is defined as ... shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is $0$ $2\pi$ $4\pi$ $8\pi$
go_editor
asked
in
Calculus
Feb 19, 2020
by
go_editor
5.0k
points
gateme-2020-set1
calculus
vector-identities
0
answers
0
votes
GATE2019 ME-2: 26
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $- \dfrac{\pi}{2} \\$ $\dfrac{\pi}{3} \\$ $\dfrac{\pi}{2} \\$ $\pi$
Arjun
asked
in
Calculus
Feb 9, 2019
by
Arjun
27.4k
points
gateme-2019-set2
calculus
vector-identities
0
answers
0
votes
GATE ME 2012 | Question: 25
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by $\dfrac{1}{\sqrt{2}} \hat{i} +\dfrac{1}{\sqrt{2}} \hat{j} \\$ ... $\hat{k} \\$ $\dfrac{1}{\sqrt{3}} \hat{i} +\dfrac{1}{\sqrt{3}} \hat{j} +\dfrac{1}{\sqrt{3}} \hat{k}$
Andrijana3306
asked
in
Calculus
Mar 20, 2018
by
Andrijana3306
1.5k
points
gateme-2012
calculus
vector-identities
0
answers
0
votes
GATE2018-2-28
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, its ... $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\ $ $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $
Arjun
asked
in
Calculus
Feb 17, 2018
by
Arjun
27.4k
points
gateme-2018-set2
calculus
vector-identities
0
answers
0
votes
GATE2018-1-27
The value of the integral over the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\overrightarrow{n}$ is the normal to the surface $S$, is $V$ $2V$ $3V$ $4V$
Arjun
asked
in
Calculus
Feb 17, 2018
by
Arjun
27.4k
points
gateme-2018-set1
calculus
surface-integral
vector-identities
0
answers
0
votes
GATE2017 ME-2: 2
The divergence of the vector $-yi+xj$ is ________.
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set2
numerical-answers
calculus
vector-identities
divergence-and-curl
0
answers
0
votes
GATE2017 ME-1: 27
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set1
numerical-answers
calculus
vector-identities
0
answers
0
votes
GATE2016-3-53
A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point is $(−6, 3,−9)$ $(−6,−3,−9)$ $(6, 3,−9)$ $(6, 3, 9)$
Arjun
asked
in
Calculus
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set3
calculus
vector-identities
0
answers
0
votes
GATE2016-3-27
The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ and ${\overline{r}}'$ is ... $x-y$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
Arjun
asked
in
Calculus
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set3
numerical-answers
calculus
vector-identities
initial-and-boundary-value-problems
0
answers
0
votes
GATE2016-2-26
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \varphi .d\overrightarrow{r}$ on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$. The curve $C$ ... . The value of the integral is ________
Arjun
asked
in
Calculus
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set2
numerical-answers
calculus
integrals
vector-identities
0
answers
0
votes
GATE2016-1-53
The figure below represents a triangle $PQR$ with initial coordinates of the vertices as $P(1,3)$, $Q(4,5)$ and $R(5,3.5)$. The triangle is rotated in the $X$-$Y$ plane about the vertex $P$ by angle $\theta$ in clockwise direction. If sin$\theta$ = $0.6$ and cos$\theta$ = $0.8$, the new coordinates of the vertex $Q$ are $(4.6, 2.8)$ $(3.2, 4.6)$ $(7.9, 5.5)$ $(5.5, 7.9)$
Arjun
asked
in
Calculus
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set1
calculus
vector-identities
0
answers
0
votes
GATE2015-3-24
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$(\phi \overrightarrow{V})$ = $\bigtriangledown$($\phi$ ... $\overrightarrow{V}=0$ Div($(\phi \overrightarrow{V})$ ) = $\phi$ Div$\overrightarrow{V}$
Arjun
asked
in
Calculus
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2015-set3
vector-identities
calculus
engineering-mathematics
0
answers
0
votes
GATE Mechanical 2014 Set 4 | Question: 44
Consider a velocity field $\overrightarrow{V}=k(y\hat{i}+x\hat{k})$ , where $K$ is a constant. The vorticity, $Ω_Z$ , is $-K$ $K$ $-K/2$ $K/2$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set4
calculus
vector-identities
velocity
0
answers
0
votes
GATE Mechanical 2014 Set 3 | Question: 3
Divergence of the vector field $x_2z\hat{i}+xy\hat{j}-yz\hat{k}$ at $(1,-1,1)$ is $0$ $3$ $5$ $6$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set3
calculus
vector-identities
divergence-and-curl
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 3
Curl of vector $\overrightarrow{F}=x^2z^2\hat{i}-2xy^2z\hat{j}+2y^2z^3\hat{k}$ is $(4yz^3+2xy^2)\hat{i}+2x^2z\hat{j}-2y^2z\hat{k}$ $(4yz^3+2xy^2)\hat{i}-2x^2z\hat{j}-2y^2z\hat{k}$ $2xz^2\hat{i}-4xyz\hat{j}+6y^2z^2\hat{k}$ $2xz^2\hat{i}+4xyz\hat{j}+6y^2z^2\hat{k}$
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set2
calculus
vector-identities
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 5
Which one of the following describes the relationship among the three vectors, $\hat{i}+\hat{j}+\hat{k}$ , $2\hat{i}+3\hat{j}+\hat{k}$ and $5\hat{i}+6\hat{j}+4\hat{k}$ ? The vectors are mutually perpendicular The vectors are linearly dependent The vectors are linearly independent The vectors are unit vectors
Arjun
asked
in
Calculus
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set1calculus
vector-identities
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