Recent questions tagged vector-calculus / GO Instrumentation

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GATE2020: 1
The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrightarrow{a} and\;\overrightarrow{b}$ on that plane such that $\overrightarrow{a}\neq \alpha \overrightarrow{b}$ for any scalar $\alpha$. A vector perpendicular to both $\overrightarrow{a} and\;\overrightarrow{b}$ is ___________ $\hat{k}$ $\hat{i}-\hat{j}$ $-\hat{j}$ $\hat{i}$

The unit vectors along the mutually perpendicular x,y and z axes are $\hat{i},\;\hat{j}\; and \;\hat{k}$ respectively. Consider the plane $z=0$ and two vectors $\overrigh...

soujanyareddy13

2.7k points

soujanyareddy13 asked Nov 3, 2020

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GATE2019 IN: 1
$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\widehat{k}}$ and $\overrightarrow{b}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ – ${\widehat{k}}$, the vector $\overrightarrow{c}$ is parallel to $\widehat{i}+2\widehat{j}+3\widehat{k}$ $2\widehat{i} + \widehat{j}$ $2\widehat{i} – \widehat{j}$ $4\widehat{k}$

$\overrightarrow{a}$,$\overrightarrow{b}$,$\overrightarrow{c}$ are three orthogonal vectors. Given that $\overrightarrow{a}$ = ${\widehat{i}}$ + 2${\widehat{j}}$ + 5${\wi...

Arjun

2.9k points

Arjun asked Feb 10, 2019

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3

GATE2019 IN: 2
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightarrow{\bigtriangledown}$ x $\overrightarrow{A}$| is -1 0 1 $\infty$

The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...

Arjun

2.9k points

Arjun asked Feb 10, 2019

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4

GATE2016-4
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______. $(i-2j+k)$ $(-i+2j-k)$ $(0i+0j+0k)$ $(4i+3j+5k)$

The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______.$(i-2j+k)$ $(-i+2j-k)$$(0i+0j+0k)$$(4i+3j+5k)$

Milicevic3306

7.9k points

Milicevic3306 asked Mar 26, 2018

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5

GATE2014-4
A vector is defined as $f=y\hat{i}+x\hat{j}+z\hat{k}$ where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system. The surface integral $f.ds$ over the closed surface S of a cube with vertices having the following coordinates: $(0,0,0), (1,0,0),(1,1,0),(0,1,0),(0,0,1),(1,0,1),(1,1,1),(0,1,1)$ is __________.

A vector is defined as $$f=y\hat{i}+x\hat{j}+z\hat{k}$$where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system.The surface integral $f....

Milicevic3306

7.9k points

Milicevic3306 asked Mar 25, 2018

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6

GATE2013-5
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$? If $\Delta.E=0,\;E$ is called solenoidal If $\Delta \times E=0,\;E$ is called conservative If $\Delta\times E=0,\;E$ is called irrotational If $\Delta.E=0,\;E$ is called irrotational

For a vector $E$, which one of the following statements is $\text{NOT TRUE}$?If $\Delta.E=0,\;E$ is called solenoidalIf $\Delta \times E=0,\;E$ is called conservativeIf $...

Milicevic3306

7.9k points

Milicevic3306 asked Mar 25, 2018

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7

GATE2018IN: 26
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$\overrightarrow{k}$, the value of the linear integral $\int_c$\overrightarrow{F}$ . d$\overrightarrow{l}$ along the straight line c from (0,0,0) to (1,1,1) is 3/16 0 -5/12 -1

Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$$\overrightarrow{k}$, the value of the linear integral $\int_c$$\ove...

gatecse

1.4k points

gatecse asked Feb 20, 2018