University

Mathematics

accuracy

plays

Ashok Godase

4 years

Mathematics

University

Vector Calculus Quiz II

Ashok Godase

0
plays

20 questions

Show Answers

See Preview

1. Multiple Choice
5 minutes
1 pt
$\$ The vectors $\overrightarrow{a},\ \ \overrightarrow{b},\ \ \overrightarrow{c}$ are coplanar iff ________
$\overrightarrow{a}\times\left(\overrightarrow{b}\times\overrightarrow{c}\right)=0$
$\overrightarrow{a}\times\left(\overrightarrow{b}\times\overrightarrow{c}\right)=k$
$\left[\overrightarrow{a}\ \overrightarrow{b}\ \overrightarrow{c}\right]=0$
$\left[\overrightarrow{a}\ \overrightarrow{b}\ \overrightarrow{c}\right]=k$
2. Multiple Choice
5 minutes
1 pt
$\left|\overrightarrow{a}\times\overrightarrow{b}\right|$ denote ________
the area of the parallelogram
the volume of the parallelopiped
the area of the triangle
the volume of the sphere
3. Multiple Choice
5 minutes
1 pt
$\overrightarrow{a}.\ \left(\ \overrightarrow{b}\times\ \overrightarrow{c}\right)$ is defined by
Box product
Scalar Triple Product
The volume of the parallelopiped
all of the above
4. Multiple Choice
5 minutes
1 pt
If $\phi$ is a scalar valued function then $\nabla\phi$ is _______
Scalar Valued Function
Vector Valued function
5. Multiple Choice
5 minutes
1 pt
The equation of the tangent plane to the surface $\phi\left(x,y,z\right)=c$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\times\nabla\phi\ =\ 0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\cdot\nabla\phi\ =\ 0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\nabla\phi\ =\ 0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\nabla\phi\ =\ c$
6. Multiple Choice
5 minutes
1 pt
The equation of the normal plane to the surface $\phi\left(x,y,z\right)=c$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\times\nabla\phi\ =0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\cdot\nabla\phi\ =0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\nabla\phi\ =0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\nabla\phi\ =c$
7. Multiple Choice
5 minutes
1 pt
The equation of the tangent line to the curve which is the intersection of the two surfaces $\phi\left(x,y,z\right)=c_1$ and $\psi\left(x,y,z\right)=c_2$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\times\left(\nabla\phi\times\nabla\psi\right)\ =0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\cdot\left(\nabla\phi\times\nabla\psi\right)\ =0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\cdot\left(\nabla\phi\cdot\nabla\psi\right)\ =0$
$\left(\overrightarrow{r}-\overrightarrow{r_o}\right)\times\left(\nabla\phi\cdot\nabla\psi\right)\ =0$
8. Multiple Choice
5 minutes
1 pt
The curl of $\overrightarrow{f}$ is denoted by
$\nabla\times\overrightarrow{f}$
$\nabla\cdot\overrightarrow{f}$
$\nabla\overrightarrow{f}$
none of the above
9. Multiple Choice
5 minutes
1 pt
A vector f is called _______ if $div\ \overrightarrow{f}=0$
irrotational
Solenoidal
Harmonic vector
Laplacian operator
10. Multiple Choice
5 minutes
1 pt
The operator $\nabla^2$ is called
Box product
Square product
Laplacian operator
Harmonic vector
11. Multiple Choice
5 minutes
1 pt
The work done is defined by
$\int_C^{ }\ \overrightarrow{f}\cdot d\overrightarrow{r}\$
$\ \overrightarrow{f}\cdot d\overrightarrow{r}\$
$\left(\nabla\cdot\ \overrightarrow{f}\right)\cdot d\overrightarrow{r}\$
$\int_C^{ }\ \left(\nabla\cdot\overrightarrow{f}\right)\cdot d\overrightarrow{r}\$
12. Multiple Choice
5 minutes
1 pt
A vector f is called Harmonic vector if
$\nabla^2\overrightarrow{f}=0$
$\nabla\times\overrightarrow{f}=0$
$\nabla^2\times\ \overrightarrow{f}=0$
$\nabla\cdot\overrightarrow{f}=0$
13. Multiple Choice
5 minutes
1 pt
The divergence of a vector valued function is a
Vector valued function
Scalar valued function
14. Multiple Choice
5 minutes
1 pt
The curl of a vector valued function is
Vector valued function
Scalar valued function
15. Multiple Choice
5 minutes
1 pt
The $div\ \overrightarrow{f}$ is denoted by
$\nabla\times\overrightarrow{f}$
$\nabla\cdot\overrightarrow{f}$
$\nabla\overrightarrow{f}$
none of the above
16. Multiple Choice
5 minutes
1 pt
$\overrightarrow{i}\cdot\ \overrightarrow{i}\ \ne$
$\overrightarrow{j}\cdot\ \overrightarrow{j}$
$\overrightarrow{k}\cdot\ \overrightarrow{k}$
0
1
17. Multiple Choice
5 minutes
1 pt
$\overrightarrow{i}\times\ \overrightarrow{i}=$
$\overrightarrow{k}$
0
1
$\overrightarrow{j}$
18. Multiple Choice
5 minutes
1 pt
$\left(\overrightarrow{a}\times\overrightarrow{b}\right)\times\overrightarrow{c}\ =\$
$\overrightarrow{a}\times\ \left(\overrightarrow{b}\times\overrightarrow{c}\right)$
$\left(\overrightarrow{a}\times\overrightarrow{c}\right)\times\left(\overrightarrow{b}\times\overrightarrow{c}\right)$
$\left(\overrightarrow{a}\cdot\overrightarrow{c}\right)\overrightarrow{b}-\left(\overrightarrow{b}\cdot\overrightarrow{c}\right)\overrightarrow{a}$
$\left(\overrightarrow{a}\cdot\overrightarrow{c}\right)\overrightarrow{b}-\left(\overrightarrow{a}\cdot\overrightarrow{b}\right)\overrightarrow{c}$
19. Multiple Choice
5 minutes
1 pt
If $\overrightarrow{r}=x\ \overrightarrow{i}+y\ \overrightarrow{j}+z\ \overrightarrow{k}$ then $\left|\overrightarrow{r}\right|=$
$x^2+y^2+z^2$
$\sqrt{x^2+y^2+z^2}$
$\frac{1}{2}\sqrt{x^2+y^2+z^2}$
$\frac{1}{2}\left(x^2+y^2+z^2\right)$
20. Multiple Choice
5 minutes
1 pt
Let $\overrightarrow{a}$ be a unit vector then the directional derivative of $\phi$ is
$\overrightarrow{a}\times\nabla\phi$
$\overrightarrow{a}\cdot\nabla\phi$
$\overrightarrow{a}\nabla\phi$
none of the above
Answer choices
Tags
Answer choices
Tags
Explore all questions with a free account
Already have an account?

Vector Calculus Quiz II

University

Mathematics

Mathematics

University

Vector Calculus Quiz II

0 plays

20 questions

Introducing new Paper mode

0
plays