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20C- mid1review-07

20C- mid1review-07 - Math 20C Midterm Review The harder...

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Math 20 C 22 April 2007 Midterm Review! The harder problems are marked with an asterisk (*). Review Problems 1 Compute the angles between the following vectors: ( a ) 1, 2 and - 8, 4 ( b ) 5, - 3, 4 and 0, 7, - 1 ( c ) 1, 1, 0, - 1, 0 and 3, 2, - 1, - 7, 1 2 Find the area of the triangle with corners ( 0, 2, 4 ) , (- 1, - 1, 6 ) , and ( 1, 3, 1 ) . 3 If 3, 4 and 1, x form a 90 angle, find x . 4 Find the equation for the set of all points that are three times as far from ( 0, 1, 2 ) as they are from ( 4, 1, - 2 ) . 5 Compute the sine of the angle between the vectors 2, 1, 2 and 0, - 1, 3 . 6 A parallelepiped has one vertex at ( 0, 0, 0 ) and adjacent vertices at ( 1, 2, 4 ) , ( 1, 3, 9 ) , and ( 1, - 4, 16 ) . Compute its volume. 7 Find the equation of each of the planes described below: ( a ) the plane parallel to x + 7y - 9z = 5 and passing through ( 2, 2, 2 ) . ( b ) the plane perpendicular to the line of intersection of the planes x + 4y - z = 6 and 2x - y - 3z = 1 , and passing through ( 4, 0, 4 ) . ( c ) the plane parallel to the lines 3t + 5, t, 8 - t and 1 - t, 2 - t, t + 4 and passing through ( 5, 5, 1 ) .
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