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 OC. j+ 5k - 21 3 O D. i-*

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 the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

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

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

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Q: Find (u+v).(2u-v) given that u.u=4, u.v=-5 and v.v=10 Determine if u and v are orthogonal…

A: Given, u·u=4, u·v=-5, v·v=10

Q: Find (au / ay) at the point (u,v) = (√6, − 1), if x = u² + v² and y= uv. ди (2) (Simplify your…

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Q: Find curl(3z i+ 4x j+ 8y k). curl(3z i+ 4x j + 8y k) = ( )i + ( i )j+ ( )k

A: We need to find curl of given vector.

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

A: Curl

Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

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Q: Evaluate by separation of variables. dB u(1 – u?) sec² ß | du

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Q: Find curl(4z i+ 5x j + 7y k). curl(4z i + 5x j + 7y k) = ( i )i + ( i )j + ( i )k

A: Topic- Curl of a vector

Q: Ir 9- ((2, y) | 2553,1SyS 3): D then: dz dy = %3D

A: Given D={(x,y)|2<=x<=3,1<=y<=3}

Q: What is the point on y = 2 Vx that is nearest to (4, 0) ? A) (2 V7.27) B) (2, 2 Vz) C) 2/6 3 D)

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Q: 8. Use change of variables to find: a) The Jacobian if x=(u+3v), y =; -(v- 2u).

A: We will use concept of change of variables.

Q: Find u· v. u = i - 9j v = -5i +j u.v = 45ji

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Q: mTQ = %3D mQR = %3D U 44 mTS %3D T. R 25 MSQR %3D MRQT %3D

A: Problem 1   Problem 2

Q: OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv -…

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Q: u = 5i + 4j + k v = i+j+4k w = i+ 8j + 9k

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Q: find the distance d(u, v) between u and v in the given exercise.

A: We need to find the distance between the two vectors.

Q: Parametrize y = -x2 + 4 in terms of u and v %3D

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Q: Let f (z) =iz-7x. Which of the following is correct ? oiu, = -7 v, i u =- y i u =7 v oi4 = - 7 v iu=…

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Q: Find curl (9z i + 10x j+ 6y k). curl(9z i+ 10x j + 6y k) = ( i )i + (i j +( )k

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Q: 1 -dz O Vīo O vī2 VīI 6,

A: By see this solution below

Q: make my dv/dt = 56.55cm^3/s being a 1/3 of the filled sphere as the final answer.  Is this correct…

A: Given : cone is filling with liquid For cone :  R= 6cm H=20cm Now as liquid is pouring  h increasing…

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

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Q: cosh(3z) dz COS Sc z(z2 + 9) C

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Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: Find curl (9z i + 10x j+ 7y k). curl (9z i+ 10x j + 7y k) = ( i Di + ( i Oj + ( 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 curl(6z i + 7x j+ 6y k). curl(6z i+ 7x j+ 6y k) = ( i )i + ( i )j +(i )k

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

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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: f(2ecz tan z - 6z")dz=_ • tan z+z+e secz+z+e • secz-z+e - secz-z+c •- secz+z+e

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Bef(u, v) = uv and v calculae %3D + vu- dvðu?

A: To find- Be fu, v = uv and v calculate u∂3f∂u3 + vu∂3f∂v ∂u2.

Q: Compute D P(1,2) in the direction of v =. Please round your answer to 4 decimal places.

A: According to company rule we can answer only first question and rest can be reposted.

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

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Q: ux v of u = 2i + 3j, v = -i + j is *

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Q: 2- SSi dA A A-{(,3):x7, ソプ andy=x, xy=6,火=8 14.4)' %3D Ans (448) Az ーに

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Q: Be u = x2 + yz, where x = rsin(t), y = rcos(t) and z = rsin2(t), calculate: ∂u/∂r and ∂u/∂t

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Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

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Q: 1 dz where C is the cirlce z - 2=1.5. Evaluate : 4 1 C 8 Tti -8Ti 4 Tti

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Q: a = i+3j- k, 6= 31- j+ k, d = -31- j+ k, j = i+3+4k. č = 3i+j+4k %3D perpendicular to b and c, enter…

A: If we have to find the vectors to be perpendicular then their dot product should be 0. The formula…

Q: Find curl (2z i + 3x j + 5y k). url(2z i + 3x j + 5y k) = ( i )i + ( )j + ( 3 )k

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

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Q: Let f (z) =iz - 7x. Which of the following is correct ? oi4 = - 7 v, и 3D — olu =7 v oi4 = - 7 v,…

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Q: Let f (z) =iz – 7x. Which of the following is correct ? oių =7 v i u, i u = -7 v i u u = - 7 v oi",…

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Q: Solve Utt - c?uxx = 0, –n 0, %3D u(x, 0) = f(x), u(-n, t) = 0 = u(n, t), ux(-n, t) = 0 = ux(n, t).

A: Given: The PDE is utt-c2uxx=0 , -π<x<π,t>0.

Q: aw Find ди dw. and if w = x³ + In (-) + y, x = u? dv -+ 5 and %3D wwww y = 3v + 5u and point…

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Q: et V xu u = (1,3,-3), v = (4,0,2) e l -3 %3D ......

A: Given:            u=1,3,-3            v=4,0,2 The cross product of two vectors is…

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.