Chapter 10: Q. 15 (page 824)
If the triple scalar product is equal to zero, what geometric relationship do the vectors u, v and w have?
Short Answer
The triple scalar product is equal to zero if and only if u, v and ware coplanar.
Chapter 10: Q. 15 (page 824)
If the triple scalar product is equal to zero, what geometric relationship do the vectors u, v and w have?
The triple scalar product is equal to zero if and only if u, v and ware coplanar.
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Get started for freeIn Exercises 36–41 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 Lagrange’s identity? How is it used to understand the geometry of the cross product?
If u and v are nonzero vectors in , what is the geometric relationship between and ?
Consider the sequence of sums
(a) What happens to the terms of this sequence of sums as k gets larger and larger?
(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).
Find a vector in the direction opposite to and with magnitude 3.
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