1) Find two-space vector u if |||| = 6 & = 135° and if...

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1) Find two-space vector u if |||| = 6 & = 135° and if Ili - = 4 & Qu-u = 300°. 2) Find a unit vector in the direction i if i is the vector from P(2,1, -3) to Q(-1,0,4). Then, find c such that vector PR is orthogonal to i where R(c,c,c). 3) Find the angle between i &P if F(t) = cost i - 4sint j + t k. Round your result to four 6 significant digits. 4) Find the general equation of the plane that is determined by points (1, 2, -3), (2, 3, 1), and (0, -2,-1). 5) Find the general equation of the plane that is determined by the following lines: x-6 y+1 z = = and 2 2 1 6) Find a set of parametric equations for the line that passes through the points (2, 0, 3) and (4, 3, 3). Then, state the restriction on the parameter (as an inequality) for the line segment joining the points. 7) Use d = proi ORxQS or to find the distance between point p(5,: 3, 4) and the plane given by 6x+2y-z-5=0. 8) Sketch the cylindrical surface given by Z - 1 In addition to sketch of the surface in 3-space, be a sure to include a separate sketch of the generating curve in 2-space. Be sure to label the axes. 9) Write an equation for the surface of revolution that is determined by revolving the curve (in the yz- plane) given by 64y3 = z2 around the z-axis. (OVER) 10) Consider the surface that is given by z²+y²-x²=1 a) Sketch each of the three coordinate traces on separate systems of axes. Determine all x-,y-, and z-intercepts. y Z Z X y b) Name the surface (ellipsoid, elliptic paraboloid, hyperboloid of one sheet, and so forth). c) Sketch the surface. Be sure to label the axes.

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