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Unformatted text preview: P (1 , 1 , 1), Q (2 , , 1) and R (3 ,1 , 4) and get PQ = ij and PR = 2 i2 j + 3 k . The area of the triangle is equal to  PQ × PR  / 2 = 3 √ 2 / 2. Problem 5. Find the volume of the parallelepiped determined by the vectors a , b and c where a = i + jk , b = ij + k , c = 2 i2 j + 3 k . Solution: The volume is equal to the absolute value of the triple product abc . Thus V = ± ± ± ± ± ± 1 11 11 11 1 1 ± ± ± ± ± ± = 4 , since the determinant is positive. 1 Problem 6. A wagon is pulled a distance of 100 m along the horizontal path by a constant force of 50 N. The handle of the wagen is held at an angle of 30 ◦ above the horizontal. How much work is done? Answer: W = F · S = 50 · 100 cos 30 ◦ = 5000 √ 3 / 2 Nm....
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 Fall '08
 Keeran
 Calculus, Linear Algebra, Vectors, Vector Space, Force

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