3. Let V = 6xy?z³ + 5 In(x² + y? + 3z²)V in free space. Evaluate each of the following quantities at P(2,3, –1), find: a. V b. E c. |J|| d. D

Q: Given U(x; y) = In(1+ xy³), show that 2! dxðy

A:

Q: Determine integers j, k, u and v so that the set S = {(j+kn, u + vn) : n E Z} is equal to the set T=…

A: Equation  157x+107y = 1 is a linear Diophantine equation (ax + by = c). Here , a = 157 b = 107 and c…

Q: If ||V|| = 5, ||W|| = 6 and -a < V ·W < a, then the value of a is equal to: О а. 30 O b. 10 О с. -30…

A:

Q: Evaluate (yzi+yj+zzk) - dA, where S is the boundary of the cube defined by -1<IS2,-1 SUS1, and 0<…

A: We can use gauss divergence theorem to evaluate the surface integral.

Q: Q.2. Proof that V= u8--

A:

Q: 3. Which of the following is logically equivalent to [(-p V q)^(¬p Vg) ^(¬p Vr)]→[[p V q)^(-p vq)…

A:

Q: Suppose A if A and A" have different left null spaces then O a a= 0 O b. a= 15 Oc a= 6 1da=3

A:

Q: If|u|= 3 and|v|= 6, find|u×v|and whether u×v points into or out of the page.

A: If|u|= 3 and|v|= 6, find|u×v|and whether u×v points into or out of the page.

Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

A:

Q: Let X and Y be two T, spaces, then X×Y. :is

A:

Q: Evaluate $ c TZ e cusz -dz DCi |Z=1|=1 ✓ C₁ | 2+1 | = |

A:

Q: Consider A = (x, y,z) and B = (w,x, y). If U = A U B, which set is equal to (B\A)'? Note: B\A = B-…

A: The union of set A and B is denoted by A∪B has elements both inset A and B The complement of A has…

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

A:

Q: Which of the following statements are true? I: If F, and F, are 5-dimensional flats in R', then the…

A: Given that F1 and F2 are 5- dimensional flats in R7.

Q: Use geometry to evaluate J JR (8 - 2y)dA, where R = [O,3 ] x [0,4].

A:

Q: Determine the minimal polynomial of 2/3 – V5 ov over 0.

A: That's easy. Have a great day!!!

Q: b, c e R such that abc

A:

Q: Let xer" and ge I show that =yex is an imer product.

A: I have to show that the given relation satisfies three conditions to be a inner product

Q: Let z дz ?x дz ду = = Gexy³. Then:

A:

Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnC = 4, BnC = ¢, µ(An B) = 0. Determine µ(A UBUC).…

A: Measure

Q: Let D={(x,y,2) : x2+y2+z?s 1600, z2 o}. Evaluate - z dv.

A:

Q: Prove that o curl f dS = | 6f · dr - v ¢ x f · d$.

A:

Q: Let v = (a, b, c). Calculate v × i, v × j, and v × k.

A: given: v=a,b,c we have to calculate v×i, v×j and v×k

Q: s) Let ICS(P), 4,0, € S(P), and let I (p = 0). (a) Show that then riff I and (b) r, iff r, 0.

A: As per the question, we have to prove two statements related to the consistency of deductive…

Q: Evaluate (x – 2y + z) dS. S: z = 8 – x, 0 <x< 8, 0 < y< 7

A: Given I=∬S(x−2y+z)dSS:z=8−x,0≤x≤8,0≤y≤7

Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

A:

Q: U %3D {x\x € N Лх> 1},А %3D {-2, —1,0, 3, 6, 7, 9}, С %3D {6, 7, 8,9, 12,13}. Find: a) AnC b) AUC с)…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

A:

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

A:

Q: Find f, and f, and evaluate each at the given point. 7xy f(x, y) = (1, 1) 2x2 + 2y2" 5,X, v) %3D .…

A:

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: 10) Calculate the Jacobian, J, for the given change of variables: x = -½ (u + v) and y = (u + 3v) 2

A: