20C- mid1review-07

20C- mid1review-07 - Math 20 C 22 April 2007 Midterm...

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Unformatted text preview: 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 ) h 1,2 i and h- 8,4 i ( b ) h 5,- 3,4 i and h 0,7,- 1 i ( c ) h 1,1,0,- 1,0 i and h 3,2,- 1,- 7,1 i 2 Find the area of the triangle with corners ( 0,2,4 ) , (- 1,- 1,6 ) , and ( 1,3,1 ) . 3 If h 3,4 i and h 1,x i 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 h 2,1,2 i and h 0,- 1,3 i . 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...
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