A parallelipiped has six faces, consisting of three pairs of parallelograms across from and parallel to each other. Only four points are necessary to define such a figure; you have eight. Four vertices must be overdetermined. Knowing which four to use is the hard part of this problem. Look for sets of connecting lines that are parallel, and choose three nonparallel lines that connect to one point.
Define the vectors leading from one vertex point to three adjacent points. The vector from (9,4,3) to (7,12,2) would be -2i + 8j -1k, for example.
Then use scalar triple product rule as shown at
http://answerboard.cramster.com/calculus-topic-5-300804-0.aspx
I need to use the scalar triple product. but i don't have any vectors? how am i supposed to know what the vectors all coming from one corner are??
Q:Calculate the volume of the parallelepiped with vertices at:
(9,4,3), (7,12,2), (12,5,6), (3,-4,0), (10,13,5), (1,4,-1), (4,5,2) and (6,-3,3)
1 answer
1 answer