Find proj,u. v= 7i- 3j + k, u = - 4j + 3k 60 45 j+ -k 59 O A. 59 105 45 15 O B. 59 -i- j+ 59 59 21 Oc. 5-5k 3 +-k 12 OD. -* j+ 5 k

Q: Find curl (5z i + 6x j + 9y k). curl(5z i + 6x j + 9y k) = ( i )i + ( i )j + ( i )k

A: Given: To obtain the curl (5z i+6x j+9y k)That is to find: ∇×Fwhere here F=5z i+6x j+9y k

Q: Find curl (6z i + 7x j + 8y k). curl(6z i + 7x j + 8y k) = ( i )i + ( i )j + ( i )k

A:

Q: Q1: Prové by induction nzZ! ☆ (1- 1 htI ( Here JJ (Pi") stande for froduct) means (I- I

A: A detailed solution is given below.

Q: If u = a + j13 and v = -11 – jb, calculate Im(u + v).

A: Add the two complex numbers then write the imaginary part.

Q: Find curl (5z i + 6x j + 3y k). curl (5z i + 6x j + 3y k) = ( i )i + ( i i )k

A:

Q: Find curl(4z i + 5xj + 9y k). curi (4z i + 5xj + 9y k) = ( i )i + ( i Ok

A: We have to find out the curl

Q: Find curl(Sz i+6x j + 7y k), curl(Sz i+ 6x j + 7y k) =( i+(

A: This question van be solved using the concept of curl F.

Q: Let u = 9i - 4j and v = - 2i + 7j. Find u - v. u-v= (Type your answer in terms of i and j.)

A:

Q: Find curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

A:

Q: ×」it o2×と o, if x >I olve where gix) = { %3D

A:

Q: ar to 2x -By + 2 =

A: we have to determine such that 3x + 2y – 7 = 0 is perpendicular to 2x -By + 2 = 0.

Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: Let A = {x E Z: 8x} and let B={rEZ:12lx}. Then * ACB ВСА None of these A=B

A:

Q: Find real numbers r and y suech that 3r+2iy- ir + 5y = 7+5i. O (A) =-1, y=-2. O (B) z=-1, y = 2. O…

A:

Q: Q3: If z = f(u,v,t) = Z 3u? + v2 ,u = tet , v= te-2t Then dz at (2,2,0) at

A: Topic:- partial derivatives

Q: Q111f и %3D (1 —2ху + у?)""/2, Prove that: ди ди y əx y? u3 У ду

A:

Q: c) Show thiat det a q² -k-1)(61)-) I <a<b %3D

A:

Q: Use Cramer's ru;e to fins a solution: 5x+4y=12 3x-6y=24

A: System of equations are 5x+4y=123x-6y=24

Q: az əz az p?(r+1) Q2: Find if you know that : z = др + pre2p+3r+4t ar 'at t3

A:

Q: Find the value of zo so that dz = -2ri Izl=13 (z – z0) (z – 14i)

A: Given integral is ∫|z|=13z(z-z0)(z-14i)dz = -2πi   ---(1)

Q: Find SV. T. 15 30 R U 16 V SV %3D Submit

A:

Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

A:

Q: Find curl (5z i+ 6x j+ 8y k). curl (5z i+ 6x j+ 8y k) = ( )i + (i Oj + ( i Ok

A: Given that,    curl5z i+6x j+8y k The formula for curl is ∇×F→=i^j^k^∂∂x∂∂y∂∂zABC

Q: Find projy u. v = 7i- 3j + k, u = - 4j + 3k 105 O A. 45 15 59 '- 59 + 59k 60 45 O B. - 59i* 59k 12…

A: Given vectors are,  v=7i-3j+k and u=-4j+3k The objective is to find projvu Now, u·v=-4j+3k·7i-3j+k…

Q: Find curl(6z i + 7x j+ 6y k). curl(6z i+ 7x j+ 6y k) = ( i )i + ( i )j +(i )k

A:

Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

A:

Q: Let u = 2i - 7j, and v = - 8i + 2j. Find u - v. u-v = (Type your answer in terms of i and j.)

A:

Q: (2st +t?)ds – 3s²dt = 0,when s = 1, t = -1 8st3 = (s – t)? s³t = (t – s)* %3D 8st3 = (t – s)³ o t =…

A:

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = ( i Di + ( i Oj + ( )k

A:

Q: Find curl (8z i + 9xj+4y k). curl(8z i + 9x j + 4y k) = ( i )i + ( i j+( i )k

A: topic- curl of a vector

Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

A:

Q: Q3) find tne u bait ve ctor Pointing for ACe,3) to the (0,0)

A:

Q: S g find Ju u and av Write the anuser in terms of U ty D Using the chain rele and V 2 to

A: Answer

Q: Lặi T(z) = -6zª +2² – 1 and U(z) = 2 – 4z + 3 Find T(2) + U(z). %3D OA -6z + 22+-4z +2 OB -72 +2 OD.…

A: Tx=-6x4+x2-1  &amp;  Ux=2x3-4x+3

Q: Find projy u. v = 7i-3j+ k, u = -4 j+ 3 k 60 45 j+ k 59 59 O 105 i- 59 45 15 k 59 59 9 9. +k

A:

Q: Q5: Let A = 7i – 4j + 2k and B -3i + 6j – 2k. %3D %3D - Find A + B, |A – 2B|, A × B?

A: Given: A=7i-4j+2k  and B=-3i+6j-2k

Q: O show thet fu) =2a +3b is Candin Uous where a, b are Constants.

A:

Q: 6e? Evaluate dz by residue theorem, 9z4 + 45z3 where C'is the contour z = 2

A:

Q: zlanstriduz.n 20 9. Hx) %3D 2. 7. a tom Where a and 6= %3D %3D

A: To find  the values of a and b.

Q: = 3r and Express and ds interms of r and s, where w = x² + y?, x = r – s and y = r+s. dw 5r and as…

A:

Q: Let u = x + 7y and v = x - y. Subtracting v= x - y from u = x + 7y, we get y = Adding u =x + 7y and…

A: Given:      Let u=x+7y              v=x-y Subtracting v=x-y from u=x+7y, we get…

Q: Q) Consider (Z12, +).Then (6) U (9) = %3D i. {0,6} شيء مما بالأعلى .ب Ĉ. {3) J. {0} o. {0,3,6,9}

A: We have to solve given problem:

Q: Let u=3i|-2j and v=-4i+5j Find 2 u +3j find ||u||

A: We have to find norm u

Q: %3D If MZJKL = (8x- 6)° and mJML = (25x- 13), find mJML. %3D K J M

A:

Q: Find curl (3z i + 4x j+ 7y k). curl (3z i+ 4x j+ 7y k) = ( i )i + ( i j+ ( )k

A:

Q: dw when u = 0, v = 0 if w =x? + y x= 6u - 2v + 1, y = 5u + 4v - 3. Find

A:

Q: Compute r"(t). r(t) = (3 In (7t)i + (9t) O A. r() = --2i+54j 3 -21+54tj 3 O B. r"(t) =-i+27tj Oc.…

A: