activity chapter 13-final

activity chapter 13-final - radius 3 with the y – axis as...

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MthSc 206 Activity September 2009 Show all work and clearly indicate your answers. 1) Consider the vectors a = <6, 0, -5> and k j i b 3 2 + - = . a) Find 3 a + 5 b . b) Find the angle between a and b . 2) Find an equation of the sphere with center (2, 1, - 2) that touches the xy- plane. 3) Find parametric equations for the line through the points (2, 1, 3) and (-2, -3 ,2). 4) Find an equation of the plane that passes through the point (2,0,1) and is perpendicular to the line t z t y t x 7 3 , 8 5 , 3 5 - = - = + = . 5) a) Identify and rewrite the equation in standard form 2 2 3 z y x + - = . b) Sketch the surface. c) Find intercepts. d) Find traces for i) x = 0, ii) y = c , and iii) z = c (where c is a constant). 6) Write an equation or inequality that represents all points on and inside a circular cylinder of
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Unformatted text preview: radius 3 with the y – axis as its axis. 7) Are the lines L1: 3 3 1 4 5 4 x y z---= = and L2: 6 7 2 1 1 3 x y z---= = skew or parallel? Do they intersect? Justify your answer. 8) Consider the lines L1: 2 , 3, 1 4 x t y z t = + = = - -and L2: 5 , 3 2 , 1 4 x t y t z t = -= + = + a) Find a unit vector u perpendicular to L1 and L2. b) Find a vector v of length 3 perpendicular to L1 and L2 but in the opposite direction of u . 9) Find a vector r (in standard position) with terminal point A (-9, -8, 2). 10) A bicycle pedal is pushed by a foot with a 60 N force as shown. The shaft of the pedal is 17 cm long. Find the magnitude of the torque about P ....
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