Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: Which of the space curves below describes the vector-valued function r(t) = (t + 15, e0.08t cos t,…

A: The given parametric equation of the curve is  where  is the parameter.To determine which of the…

Q: Let S be the paraboloid y = x^2 + z^2. Find a parametric representation for S and its tangent plane…

A: The given data is: Let S be the paraboloid y=x2+z2 Find a parametric representation for S and its…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation 2x+y+2 = 4 0=0

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Q: (1) Let T be the triangle in the xy-plane with vertices at (0,0), (0,2) og (2,2). Calculate the…

A: Let T be the triangle in the xy-plane with vertices at (0,0), (0,2) og (2,2). Calculate the double…

Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: 219. The diagram at right shows a rectangular solid, two of whose vertices are A = (0, 0, 0) and…

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Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0),…

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Q: ¹ is not linearly homeomorphic to P if 1 < p ≤ 0.

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Q: F(x.y)= (v; (ス)x(0,0) f(x,y). ; (x.v) 0; (x.y) - (0,0) Given the funclion aboue, fuid the…

A: Consider a function fx,y. The directional derivative of the function in the direction of a unit…

Q: please help thank you so much

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Q: Let c denote an arbitrary constant. Determine the orthogonal trajectory of x+xIn(y) =c that passes…

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Q: 8. let C be the curue space ret) = (e*,2et ,2et ),0s ts lnca) the rength of C is

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Q: Give a acalar equation for a plane at distance 6 from the plane P with equation x+2y+2z = 5. 0-0

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Q: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

Q: 3. Triangle DEF with vertices D(0, 6). E(3.5), and F(1, 1): 90° counterclockwise about the point…

A: Rotation is a rule of transformation. Through this transformation, one can produce a new image by…

Q: Assume that span(R) = RS. What is the payoff of the portfolio Zg = R¹ (RR¹) −¹ es when es € R$ is a…

A: Given: The portfolio, zs=RTRRT-1esTo find: The payoff of the portfolio zs.

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…