a) If A=xz' i-2x²yz j+2yz k, find VxA (curl A) at the point (1,-1,1).

Q: The curl of- yi+z+xR"

A: In this question, we find the curl of the vector function by using the determinant method.

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: e'ス+×cos(2) 3. (o'1'e)と Flsye)-xをえゃxそsQe)s Find Curl at

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Q: If F(x, y, z) = (x²z, –2xz, yz), then curl F(6, –3, 1) equals %3D O (12, 39, –5) O (9,34, 2) O (13,…

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Q: 2. Find a formula for curl(curl(u)) in terms of (x1,02, X3) and (e, e2, e3) if u = uje1 + Uze2 +…

A: We will use the basics of vector calculus to answer this question in detail. Below is the…

Q: 18)Find curl F and div F if F(x,y,z) = exsiny i + esinz j + e²sinx k

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Q: 8. Which of the following is the curl of F = (2xy +1, x² + 2yz, y² – 2 )? %3D а. 0 b. 1 с. -1 d. 2

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Q: Find the curvature and the radius of curvature at the stated point. NOTE: Enter the exact,…

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Q: Current Attempt in Progress Find curl(6z i + 7x j + 9y k). curl(6z i + 7x j+ 9y k) = ( i Di +( i )j…

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Q: Find the values of a, b and c that make F=-5y°z7 (ax + bx6ji - 45,8,7(4x10, 107j+ cy°z64x10, 10x7jk…

A: Given that                          F=-5y9z7ax9+bx6i-45y8z74x10+10x7j+cy9z64x10+10x7k we know that…

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: 3. Evaluate the line integral (3ry² + 6y) da, where C' is the path traced by first moving from the…

A: The given problem is to evaluate the given line integral of (3xy2+6y) over the given path C which is…

Q: (a) (b) Let V = F" and let A EMnxn (F), F is complex field. Prove that (x, y) = (4¹x, y) for all x,…

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Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

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Q: 3. When origin is shifted to (3,4) by translation of axes, find the transformed equation of 2x² +…

A: We have to solve given problems:

Q: 10. A drop of water falls on the surface z³x+z¹y² + x²y³ = 79 at the point (3, 2, 1). Find a three-…

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Q: If F = xyz i+ zxj +xy'z k then find curl F at (1, 2, – 1).

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Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

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Q: and w = x.+ 2y. y 3. Compute the inner product g (v,w) of v = . + x. ay' 2 дх ду дх Where the line…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: Let f(z)=y-2xy +i(-x+x² - y²)+z² where, z=x+iy is a complex variable defined in the whole complex…

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Q: enter-radius form of the equation of t

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Q: Let Compute дw -(-2,-2) = -(-2,-2) = მs дw St W = 2xy - 2yz + 3xz, x = st, y = est, z = t² =

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Q: (5. 2y+z2)i+ (zy? 2)j+ (2 - 3. zy)k, find curl a at the point (4,3,3). (zy²2)j+ (c) Given that a = I…

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Q: If vector T = (x+ y+1)i+ j– (x +y)k then T.curl(T )is

A: We are given vector T.

Q: m while the (2) Find the ualue of the constanl Curl of Fasie) = mxy.ge?) Ĉ + cm-7)xi+ (I-m)×2°R is…

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Q: 37.Calculate the value of r such that the line x + 2 y + z = 0 is a center-line of the conic section…

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Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…

A: FORMULA USED- For  f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr