Chapter 10: Q.16 (page 848)
Compute \(u\times v\) if \(u=i\) and \(v=2j\).
The cross product is \(2k\).
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If u, v and w are three vectors in , which of the following products make sense and which do not?
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In 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 .)
Sketch the parallelogram determined by the two vectors and . How can you use the cross product to find the area of this parallelogram?
For each function f and value x = c in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
role="math" localid="1648705352169"
In 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.
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