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Test+2+solution

# Test+2+solution - MATH 17100 28446 Test 2 solution 10/07...

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MATH 17100 28446 Test 2 solution 10/07/ 2009 1. Given the points (1, 2,3) , (1,3,6), (3,8,6) and (3,7,3) A B C D , (a) Find the distance between A and B Distance between A and B is 2 2 2 1 1, 3 2, 6 3 0,1, 3 0 1 3 10 AB  (b) Find a vector equation for the line 1 l that passes through A and B 1 1, 3 2, 6 3 0, 1, 3 AB v  Vector equation for the line 1 l that passes through A and B is 1, 2,3 0,1,3 A t t r r v (c) Find parametric equations for the line 1 l . From the components of the vector equation in (b), , , 1, 2,3 0,1,3 x y z t , we obtain the parametric equations for the line 1 l : 1 0 , 2 1 , 3 3 x t y t z t 1, 2 , 3(1 ) x y t z t (d) Find symmetric equations for 1 l . Eliminating the parameter from the parametric equations in (c), we obtain the symmetric equations for 1 l : 3 1, 2 3 z x y (e) Find the equation of the plane 1 that contains A , B and C . We found from (a), 0,1, 3 AB  3 1, 8 2, 6 3 2, 6, 3 AC  Plane 1 has normal 0, 1, 3 2, 6, 3 ( 3 ) (2 6 3 ) AB AC n j k i j k   2 3 6 18 15 6 2 15, 6, 2   k i j i = i j k =

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Equation of plane 1 is A A A ax by cz ax by cz 15 6 2 15(1) 6(2) 2(3) 9 x y z       15 6 2 9 x y z (f) Find the distance from the point C to the line 1 l 0,1, 3 AB v  is along line 1 l , 2, 6, 3 AC  from (e) Distance from the point C to line 1 l is 0,1, 3 0,1, 3 ˆ ˆ ( ) 2, 6, 3 2, 6, 3 10 10 AB AC proj AC AC AC v v      0,1, 3 0 6 9 15 3 9 2, 6, 3 2, 6, 3 0,1, 3 2 0, 6 , 3 10 2 2 10 10 2 2 2 9 3 1 1 2, ,
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Test+2+solution - MATH 17100 28446 Test 2 solution 10/07...

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