A = (2, -4) and B = (-3,3). Determine the distance between points A and B and find their polar coordinates.

A small block slides at a speed von a horizontal surface. Knowing that h=04 m, determine the required speed of the block if it is to leave the cylindrical surface BCD when 0 = 35". The required speed of the block to leave the cylindrical surface is m/s

Find a vector equation for the line through the point (-4, 8, 2) perpendicular to the plane –7x – 7y + 7z = 16. with -o < t<∞ 7(1) =

Given the points in space, A = (4,2,– 3), B = (-2,5,1), and C = (5,1,– 2) A) Find a parametric set of equations for the line through point A parallel to the line through points B and C. B) Find the equation of the plane containing points A, B, and C using a vector approach (from chapter 11). C) Find the coordinates of a point on the plane other than A, B, or C which does not lie on a coordinate axis. (no 0 coordinates)

Find the divergence and curl of each of the following vector functions: 1. S = < xy, 2yz, 3zx > 2. E = < y^2, (2xy+z^2), 2yz >

1.3 Determines the value of m so that the vectors ū = [-2,6,4] and v = [m,9,6] are: A) collinear B) orthogonal