A. Consider complex plane C and identify it with a plane R2 in 3D-space Rº with...
Use the following steps to find the general equation of the plane that intersects the surface f (x, y) ye2x-y+5 at f(-1,3): = the y Choose any vector ū, u 0, in the xy-plane that is parallel to neither the x-axis nor product to show that i is parallel to neither axis. a) axis. Use a cross Find Df1,3) b) Choose any vector v, v 0, in the xy-plane that is orthogonal to u. Use the dot product to show...
Part B Please 2. Consider a point (xo, y0, 2o) in space and a vector (a, b, c). We can use this vector to define a plane as the set of all points (x,y, z) such that the vector (x - xo, y - yo, z - zo) connecting (z, y,z) with (xo, Yo, 20) is orthogonal to (a, b, c) (the normal vector to the plane). (a) Use a dot product to write the equation of a plane through...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
4. (4.5 pts) Consider a 3D electromagnetic plane wave in vacuum, described in usual complex form by, (r, t) = Ēelkr-wt) in which ło = Epein/2y. Where k = -kx is the wave vector (assume k > 0) and w > 0 is the angular frequency. As usual, the real field is Er, t) = ReLEr, t)] (a) In which direction is the wave propagating? In terms of the given values k and w, what is the speed, wavelength, and...
If C is the curve given by r (t) = (1 + 4 sin t)i + (1+2 sin2t)j + (1 + 3 sin3t) k, 0≤t≤π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.
If C is the curve given by r(t) = (1 + 3 sin t)i + (1+2 sin2t) j + (1 + 5 sin3t) k, 0 ≤t≤π/2 and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.
please help 2. A metal rod with a length of 25.0 cm lies in the xz-plane and makes an angle of 15.00 with the positive x-axis and an angle of 75.0° with the positive z-axis. The rod is moving in the plane at a direction perpendicular to its length with a speed of 7.50 m/s. The rod is in a uniform magnetic field of B3(0.120T)/^ + (0.260T)/^-(0.0500T)k". what is the magnitude of the emf induced in the rod? Start with...
Please write neat and explain thank you. This problem concerns embedding the complex plane C with elements zx iy in the Riemann sphere defined in 3-dimensional space R' with coordinates (X,Y,Z) as the set of points satisfying X2 + Y2+22 = 1, which is known as the unit sphere and denoted by S2,or in the context of stereographic projection of the complex plane into the sphere, often referred to as the extended complex plane and denoted by C. We identify...
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) = f(u,v) i + g(u,v) j+h(u, v) k is the plane through P, normal to the vector ru (uo.VO) XIV(40.VO) the cross product of the tangent vectors ru (uo. Vo) and rv (uo.VO) at Pg. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. (573 15...
The magnetic field in a region of space is given by: Ba(x2+22)7+(y2+22)7+(x2+z2)k) where alpha is some constant, x, y, and z are the coordinates in space about the origin and i, j, and k are unit vectors pointing along the x, y, and z-axes Also in the region of space is a conducting square loop with side lengths of L which is placed parallel to the xy-plane, centered on the z-axis, and has a z-coordinate of z Find an expression...