Practice Questions

Question 1

How to solve this

Answer 1

1) say what x, y and x equal

2) take the 2 partials of the parametrized function

3) take the cross product of those 2 partials

4) use tangent plane equation to get tangent plane equation

Question 2

What is the answer to this

Answer 2

2x+z =1

Question 3

How to do this

Answer 3

Div(curl) = 0, so fire hard that part

Take divergence of remaining part and solve for “a”

Question 4

How to do this

Answer 4

Use surface areas formula (pick 1 out of the 3)

Question 5

How to do this

Answer 5

Question 6

How to do this

Answer 6

Use mass of a plate formula with dxdy

Question 7

How to do this

Answer 7

1) find curl, then curl at that point

2) set dot product to 0 since orthogonal and solve for “a”

3) can now take divergence

Question 8

How to do this

Answer 8

1) state what x, y, and x are

2) take 2 partials

3) take cross product of those 2 partials

4) figure out what u and v equal (using point given)

5) use what u and v are to simplify cross product answer

6) use tangent plane formula to find equation of tangent plane

Question 9

How to do this

Answer 9

Question 10

How to do this

Answer 10

Use conservative formula to solve for “a”

Question 11

How to do this

Answer 11

Remember green’s theorem formula for AREA of a (+) SCC

Question 12

How to do this

Answer 12

Div(curl) = 0

Question 13

How to do this

Answer 13

1) gradient field means curl is zero

2) find curl

3) see if there’s a value for a that would make curl 0

4) there isn’t here since there’s STILL an “i” component

Question 14

What is radius of gyration

Answer 14

Distance from axis of rotation to a point where total mass of the body is supposed to be concentrated

Question 15

What is the formula for “region of D” (area) using Green’s

Answer 15

Question 16

Is divergence a scalar or vector

(And what does it look like)

Answer 16

Scalar

Question 17

Is curl a scalar or a vector

(And what does it look like)

Answer 17

Vector

Question 18

What is curl of a conservative vector field

Answer 18

0

Question 19

What is curl of a gradient

(and why)

Answer 19

0

(Gradients are conservative)

Question 20

What does zero flux mean for divergence

Answer 20

0 divergence

Question 21

What is div(curl)

Answer 21

0

Question 22

Equation of a sphere

Answer 22

Question 23

When to use spherical

Answer 23

When region has some symmetry

Question 24

When is the dot product 0

Answer 24

Vectors are perpendicular

Question 25

When is cross product 0

Answer 25

Parallel

Question 26

What does “centroid” mean

Answer 26

Centre of mass

Question 27

What is the answer to this

Answer 27

Question 28

How to do this

Answer 28

Question 29

How to do this

Answer 29

Question 30

How to do this

Answer 30

Question 31

How to do this

Answer 31

Question 32

How to do this

Answer 32

Question 33

How to do this

Answer 33

Question 34

How to do this

Answer 34

Question 35

How to do this

Answer 35

Question 36

How to do this

Answer 36

Question 37

How to do this

Answer 37

Question 38

How to do this

Answer 38

Question 39

How to do this

Answer 39

Question 40

How to do this

Answer 40

Question 41

What is the answer to this

Answer 41

Question 42

How to do this

Answer 42

Question 43

How to do this

Answer 43

Question 44

How to do this

Answer 44

Question 45

How to do this

Answer 45

Question 46

How to do this

Answer 46

Question 47

What is the answer to this

Answer 47

-1

Question 48

How to do this

Answer 48

Question 49

How to do this

Answer 49