nce we do not have our path as a vector, we can use Stoke's Theorem to find th nd the "curl" of the vector field. og of XF - dy A vxi = (2. - 3, s) 8 vxF = (0. 2, - 3) © vxF = (-2, 5, -3) O vxi - (0. 0, 0) e can see that the normal vector for a parabolaid is - (2x, 2y, – 1) se the value for curl from the previous question and the normal vector to find s A [v xF] -ñ = o ® [vxF] . = 4 - 6xy - 8

Q: a. F(x, y) = (2x, 2y) Matches with Plot b. F(x, y) = (-2y, 3x) Matches with Plot. C F(x, y) = (2,…

A: Graph of (a)

Q: 4. If the following vector field is irrotational (i.e. zero curl), А 3 (аху + Bz3)а, + (3x? — 62)а,…

A:

Q: In words, what is a vector field? Give some physical examples of vector fields

A: Vector feild can be defined in 2 dimensions as well as 3 dimensions.A vector field F→ in ℝ2 is an…

Q: determine whether each vector belongs to Null A where A=[1,-2,-1,0;0,1,3,-2;-2,3,-1,2]…

A: Since the result of AB  is not the zero vector, the vector B does not belong to the null space of…

Q: Discuss one of the parallels between a conservative vector fieldand a source-free vector field.

A:

Q: Use double- and half-angle formulas to find the exact value of the expression sin 22.5°.

A: Given: sin 22.5° To find: The exact value by using double and half-angle formula.

Q: Sketch the vector field. У x F(x, y) = ( - 1/2, 2/2 ) x У 20 0 2 -20 0 -2 2 2 -2 2 -2 -2 2 -2 4 3 3…

A: Step 1:

Q: points

A:

Q: Sketch the vector fields. Use a table for it.    F(x,y)=<x,y-x

A: Sketch the vector field Make a table to sketch the vector field. Table should have values (x,y)

Q: Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). OF (t) =…

A: Note that the vector equation of the line passing through two points a→ and b→is given by:…

Q: find the components of the vector −→P Q. P = (1, 0, 1), Q = (2, 1, 0)

A: Given  P=&lt;1,0,1&gt;Q=&lt;2,1,0&gt; The component form of a vector is the ordered pair that…

Q: If A and B are vector fields, prove the following: V (A · B) = (B - V) A + (A · V) B+B× (V×A)+A ×…

A:

Q: When is a vector field irrotational?

A: We have to determine when is a vector field is irrotational.

Q: -2t y= c1e -1 1

A: For the solution of the problem follow the next step.

Q: Interpret the curl of a general rotation vector field.

A:

Q: Sketch the vector field. 8 2 0 -2 0 y 0 2 0 -2 F(x, y) = (2, 2) = 2'

A:

Q: Give three equivalent properties of conservative vector fields.

A:

Q: Define the terms sink and source in vector fields.

A:

Q: Find the curl of the vector field F = . curl F = i + 3+ k

A:

Q: What are the outputs of a vector field in ℝ3?

A: What are the outputs of a vector field in ℝ3.

Q: Draw the following vector fields by drawing the vectors at every integer coordinate in the rectangle…

A: We have to draw the vector field for Fx,y=y,x and Fx,y=-1,x+y2

Q: Match each vector field with its graph. xi + yj + zk (x² + y² +2²)3/2 C# 27= = 3.7 = x² + yj D#…

A: According to the given data, match each vector field with its graph.