Find the constants a, b, c so that the vector à = (-5x – 6y + az)i + (bx + y – 2z)j + (-3x + cy – 4z)k | is irrotational and find its scalar potential.

Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

A:

Q: ) Show that F = (2xy +2³) i+x²j+3r2²k is conservative force field. Find the scalar potential of F.

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Match the vector field with its graph. F(x, y) = xi + 3yj + +x ' ||||||||||| 畫 至 X

A: Solution is given below:

Q: Find llFll and sketch several representative vectors in the vector field.

A:

Q: Match the vector field with its graph. F(x, y) = yi 址 四 場 x Q 6 電

A: F(x,y)=yi So at any point vector magnitude is same as y-cooridnate Also, if y is negative [below the…

Q: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

A:

Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

A:

Q: Find a potential function for the vector field F(x, y) = (14xy + 7y- 8, 7z + 7z). f(x, y) =

A:

Q: Determine a scalar equation for the plane that passes through the point (2, 0, -1) and is…

A:

Q: Match the vector field with its graph. F(x, y) = yi -6+

A:

Q: The magnetic field along a solenoid is conservative and given by 2xy 7- (2 x ₁-2x, (x²+1)-2). ¡−2x,…

A: Given a vector field as F=2xyx2+1-2x,lnx2+1-2 We need to find the scalar potential from which this…

Q: X, y, z) = (10y - az – 5x)i + (3by-x +8z)k + (z – 5y + 2cx)j (2) Find the real values of a,b,c that…

A:

Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

A:

Q: Find the gradient vector field of f(x,y) = x2 + y2 and sketch it.

A: Solution

Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

A:

Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

A:

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

A:

Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

A:

Q: Find the flux of the vector field V(x, y, z) = 9xy²i + 9x²yj + z³k out of the unit sphere.

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5 y -6+

A:

Q: Find the flux of the vector field F = (y, - z, x) across the part of the plane z = 4+ 2x + 3y above…

A: The given vector field is, F→=y, -z,  x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: for the vector field F = 2xz i+ (1 – 4xy² ) j led by the plane z = 6 – 2x² – 2y² and the plane

A: We have to find the following conditions according to the given information

Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

A:

Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

Q: Let v ∈ R2 be a vector in the first quadrant. Express v in terms of its coordinate vectors with…

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj -st

A: Plot the given vector Fx,y=xi+3yj.

Q: Verify that the vector field f is conservative and find its scalar potential. 3r f = + yz + 2xz) i+…

A: If the vector field f:ℝ3→ℝ3 is continuously differentiable in a simply connected domain  and curl…

Q: The vector field F = (, i, 2²) has a scalar potential in the region R= {(x, y, 2) E R³ : r² + y? >…

A: We find out true or false.

Q: Given a scalar function V(x, y) =-(x² +y² ), the directional derivative of V in the direction of the…

A:

Q: Calculate the flux of the vector field F = -2i + 5æ²j – 3k, through the square of side 2 in the…

A:

Q: b) Find the curl of the vector field, CurlF, if F = Ax²z²i– By:'j+Cz*k, where the coefficients A,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the flux of the vector field F = 2 i +3 j – 2 k through the rectangle with corners at (1,0,0),…

A:

Q: Calculate the line integral of the vector field F = -3 i+ 2j along the line from the point (4, 0) to…

A: To find the line vector of following vector fieldF→=-3i+2jalong the line 4,0 and 12, 0

Q: Find the potential function for the vector (a+1,b+1,b–1) 2.3_3 2.xy'z* dx + 3x*y°z* dy +4x²y°z° dz…

A:

Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Find the flux of the constant vector field i = -4 i – 5j- 2 k through a square plate of area 16 in…

A: The solution is given below

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given : f(x,y,z)=9x2y+5z2   To Find : Conservative Vector field by finding it's gradient

Q: Sketch some vectors in the vector field F(x, y) = 2xi + yj.

A: Given: F(x, y) = 2xi^ + yj^

Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

A:

Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

A:

Q: Find a scalar equation of the plane that passes through the points (1, 1, 1) and (2,0,3) and is…

A:

Q: Find the Duf of f(x, y,z) = z In(x+ y) + e3y on the vector u = 3i -j-4k at Po(1,0,1)

A:

Q: Find a vector-valued function whose graph is the indicated surface: the part of the paraboloid z =…

A:

Q: Find the scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

A: To Find: Scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

A:

Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…

Q: Compute the flux of the vector fieldi = -3 i+ 4j- 2 k through the rectangular region shown below,…

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.