Express in cylindrical components: (a) the vector from C(3, 2, -7) to D(-1, -4, 2); (b) a unit vector at D directed toward C; () a unit vector at D directed towward the origin.
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- If a charged particle of charge q� is travelling with a velocity v� in a magnetic field B,�, then the force that that charged particle feels is given by F=qv×B.�=��×�. In this case, the force F� is also a vector quantity, since it has both a magnitude and a direction. So the cross product plays an important role in physics and engineering. Now suppose that a proton with some positive charge q� is traveling in the xy��-plane with a velocity in the direction of the vector v=⎛⎝⎜3−20⎞⎠⎟�=(3−20) and that the magnetic field B� is a uniform field pointing straight up in the z� direction, perpendicular to the xy��-plane. Then the direction of the force that the moving proton feels is in the directionDetermine the scalar equation of a plane through the point (3, 0, 4) and having normal vector n= (2, -1, 4).The magnitude of the cross (vector) product between unit vector theta and unit vector rho (unit vector in cylindrical coordinates) is equal to or can be simplified into?