Quiz1_sol

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

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online