Chapter 10: Q.24 (page 848)
Compute the lengths of the four diagonals of the parallelepiped
determined by \(u=i\), \(v=2j\), and \(w=2k\).
Short Answer
The lengths of the four diagonals are \(5,5,2\sqrt2,\text{ and }3\).
Chapter 10: Q.24 (page 848)
Compute the lengths of the four diagonals of the parallelepiped
determined by \(u=i\), \(v=2j\), and \(w=2k\).
The lengths of the four diagonals are \(5,5,2\sqrt2,\text{ and }3\).
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In Exercises 36โ41 use the given sets of points to find:
(a) A nonzero vector N perpendicular to the plane determined by the points.
(b) Two unit vectors perpendicular to the plane determined by the points.
(c) The area of the triangle determined by the points.
(Hint: Think of the -plane as part of .)
What is the definition of the cross product?
What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v and w? How do you find the volume of the parallelepiped determined by u, v and w?
In Exercises 30โ35 compute the indicated quantities when
Find the volume of the parallelepiped determined by the vectors u, v, and w.
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