Calculus
7th Edition
ISBN: 9781524916817
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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For the system consisting of the lines:
and
71 = (-8,5,6) + t(4, −5,3)
72 = (0, −24,9) + u(−1, 6, −3)
a) State whether the two lines are parallel or not and justify your answer.
b) Find the point of intersection, if possible, and classify the system based on the
number of points of intersection and how the lines are related. Show a complete
solution process.
3. [-/2 Points]
DETAILS
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SESSCALCET2 7.4.013.
Find the exact length of the curve.
y = In(sec x), 0 ≤ x ≤ π/4
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Sind dy max
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at 0.75m from A
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Chapter 9 Solutions
Calculus
Ch. 9.1 - Prob. 1PSCh. 9.1 - Prob. 2PSCh. 9.1 - Prob. 3PSCh. 9.1 - Prob. 4PSCh. 9.1 - Prob. 5PSCh. 9.1 - Prob. 6PSCh. 9.1 - Prob. 7PSCh. 9.1 - Prob. 8PSCh. 9.1 - Prob. 9PSCh. 9.1 - Prob. 10PS
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