4. Match the vector fields given below with their plots. (a) F(x,y, z) =< x, Y, z > (b) F(x, y, z) =< 0, 1,0 > (c) F(x, y, 2) = I² + y²' VI² + y² - (d) F(x, y, z) = (x² + y² + z²)3/2' (x² + y² + z²)3/2' (2² + y² + z?)3/2, Field (I) Field (II) Field (III) Field (VI)

Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: (a) Let V = Rª and let 3 be the standard dot product on V. (i) Calculate B((1,0, 1,0), (0, 1,0, 1)).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Compute the directional derivatives of the following functions along unit vectors at the indicated…

A:

Q: H is the set of all vectors x = X2 in R³ with the property that X3 X1 + x2 = 0 and Xi – x2 + x3 = 0.…

A:

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…

Q: (a) Find the best approximation to ✅ by a vector of W. (b) Write as the sum of a vector in W and a…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Find a vector parametrization of the line through P = (0, -3, -2) in the direction V = (6, 4, 1)…

A: Step 1:   Step 2: Step 3: Step 4:

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional derivative gives the rate of change of a function at a specific…

Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Suppose f(x, y) = (a) ▼ ƒ(x, y) = (b) Vƒ(4,5) = (c) fu (4, 5) = D„ ƒ(4, 5) = and u is the unit…

A:

Q: Find the directional derivative of f(x,y,z) = z3-x2y at the point (4, -3, 4) in the direction of the…

A:

Q: Find T(t) ,Ñ(t),B(t), and k(t) for the vector position r(t) = (e2t cos t) i + (e2t sin t)j+ 2k when…

A: We have given r→(t)=e2tcosti+e2tsintj+2k. To find the unit tangent vector T→(t) at t=0, first…