12.3-5 - , 2 , 3) which is perpendicular to the line x = 1...

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MATH 231 Group Work Quiz Related 1. Find a · b , a × b , proj a b , and comp a b . Can you draw any conclusions about a and b from these results? (a) a = h 2 , 4 , - 8 i and b = h 3 , 6 , - 12 i . (b) a = h 1 , 2 , 4 i and b = h- 2 , 3 , - 1 i . (c) a = h cos t, - sin t, 3 i and b = h- cos t, sin t, 1 i . 2. Find the angle between a diagonal of a cube and a diagonal of one of its faces. 3. Find the following: (a) A line through (1 , 2 , 3) and perpendicular to h 2 , 1 , 1 i and h 1 , 0 , 0 i . (b) A plane through the point (1 , 2 , 3) and perpendicular to h 2 , 1 , 1 i . (c) A plane through the point (1 , 2 , 3) and perpendicular to the line x = 1 + t , y = 1 - 2 t , z = 4 t . (d) A plane containing the line x = 1 + t , y = 1 - 2 t , z = 4 t and the point (1 , 2 , 3). (e) A plane containing the line of intersection of the planes x - z = 2 and - 8 x + y = 0 and perpen- dicular to the plane 2 x + y - z = 3. (f) The parametric equations for the line through the point (1
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Unformatted text preview: , 2 , 3) which is perpendicular to the line x = 1 + t , y = 1-2 t , z = 4 t and intersects it. 4. Show that, if u + v and u-v are orthogonal, then | u | = | v | . Not Quiz Related 1. Classify and sketch the following surfaces: (a) z = x 2 + y 2 (b) z 2 = x 2 + y 2 (c) 1 + z 2 = x 2-y 2 (d) 1 + z 2 = x 2 + y 2 2. What is the domain of the vector function r ( t ) = D 2-t, ln t, t 2-1 t-1 E ? 3. At what point(s) do the curves r ( t ) = t 2 ,t 2 + 1 , 4 t and s ( t ) = t-4 , 1 2 t,- t 2-4 intersect? 1...
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