Linear Algebra Solutions 85

Linear Algebra Solutions 85 - , 3 + 7) = (7 ,-1 , 10) . 6....

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Hence P = (16 / 7 , 29 / 7 , 3 / 7). The equation t/ (1 - t ) = - 2 / 5 gives t = - 2 / 3 and hence P = 2 3 - 1 - 2 3 1 4 5 = 4 / 3 1 / 3 - 13 / 3 . Hence P = (4 / 3 , 1 / 3 , - 13 / 3). 5. An equation for M is P = A + t - BC , which reduces to x = 1 + 6 t y = 2 - 3 t z = 3 + 7 t. An equation for N is Q = E + s - EF , which reduces to x = 1 + 9 s y = - 1 z = 8 + 3 s. To Fnd if and where M and N intersect, we set P = Q and attempt to solve for s and t . We Fnd the unique solution t = 1 , s = 2 / 3, proving that the lines meet in the point ( x, y, z ) = (1 + 6 , 2 - 3
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Unformatted text preview: , 3 + 7) = (7 ,-1 , 10) . 6. Let A = (-3 , 5 , 6) , B = (-2 , 7 , 9) , C = (2 , 1 , 7). Then (i) cos ABC = (-BA -BC ) / ( BA BC ) , where-BA = [-1 ,-2 ,-3] t and-BC = [4 ,-6 ,-2] t . Hence cos ABC =-4 + 12 + 6 14 56 = 14 14 56 = 1 2 . Hence ABC = / 3 radians or 60 . 88...
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