(a)
To evaluate: The component of u along v in terms of the dot product and sketch the component.
(a)
Answer to Problem 3E
The component of u along v in terms of dot product is
Explanation of Solution
Section 1:
The component of u along v is,
Substitute
Thus, the component of u along v in terms of dot product is
Section 2:
The component of u along v is,
The angle between
Figure (2)
Thus, the Figure (2) shows the component of u along v.
(b)
To evaluate: The projection of u onto v and sketch the projection.
(b)
Answer to Problem 3E
The projection of u onto v is
Explanation of Solution
Section 1:
The projection of u onto v is,
Substitute
Thus, the projection of u onto v is
Section 2:
The projection of u onto v is the vector parallel to v and whose length is the component of u along v.
Figure (3)
Thus, the Figure (3) shows the projection of u onto v.
Chapter 9 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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