Quiz1_sol - NAME: Spring 2011, MAC 2313, Quiz 1 UFID:...

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NAME: Spring 2011, MAC 2313, Quiz 1 UFID: Section: 3124 1. Find a unit vector that is orthogonal to both i + j and i + k . (2 points) Solution. Let v be the cross product of i + j and i + k , then we know v is perpendicular to both of them. Now v = ( i + j ) × ( i + k ) = ± ± ± ± ± ± i j k 1 1 0 0 1 1 ± ± ± ± ± ± = i - j + k , (1) and | v | = p 1 2 + ( - 1) 2 + 1 2 = 3. Hence v | v | = 1 3 i - 1 3 j + 1 3 k (2) is a unit vector that is perpendicular to both i + j and i + k . 2. Find the volume of the parallelepiped determined by the vectors a = i + j + k , b = i - j + k , and c = - i + j + k . (2 points) Solution. Since a · ( b × c ) = ± ± ± ± ± ± 1 1 1 1 - 1 1 - 1 1 1 ± ± ± ± ± ± = - 4 , (3) we know that the volume is | a · ( b × c ) | = 4. 3. Determine whether the lines L 1 and L 2 are parallel, skew, or intersecting. If they intersect, find the point of intersection. Here
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.

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