Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 9, Problem 1PE
(a)
To determine
To find:a
(a)
Expert Solution
Explanation of Solution
A Vector is a quantity that has both magnitude and direction. A vector PQ is represented as a directed line segment and an arrow with initial point
A vector is indicated by writing an arrow over the designated points
Vector PQ is the vector from
Conclusion:
Therefore, a Vector is a quantity that has both magnitude and direction.
(b)
To determine
To find: a scalar.
(b)
Expert Solution
Explanation of Solution
A scalar is a quantity that has only magnitude, not direction. In context of vectors, a scalar is described as a real number.
For example,
Conclusion:
Therefore, a scalar is a quantity that has only magnitude, not direction.
(c)
To determine
To give: an algebraic and a geometric interpretation of multiplication of a vector by a scalar.
(c)
Expert Solution
Explanation of Solution
When a scalar number c is multiplied by a vector v , the scalar multiple cv will be parallel to the vector v and has length
The scalar multiple cv points in the same direction as v if
Geometrically, assume that vector v has a magnitude of 3 units and its direction is from point P to point Q .
The scalar multiple 2v will have a magnitude of
Conclusion:
Therefore,when a scalar number c is multiplied by a vector v , the scalar multiple cv will be parallel to the vector v and has length
Geometrically, the scalar multiple 2v will have a magnitude of
(d)
To determine
To find: parallelogram rule for vector sums
(d)
Expert Solution
Explanation of Solution
The Parallelogram rule states that
Conclusion:
Therefore, the Parallelogram rule states that
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Chapter 9 Solutions
Calculus
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