Example Video Example Find the scalar projection and vector projection of b = (4, 1, 1) onto a = (-1, 3, 4). Solution Since |al = V(-1)² + 32 + 42 = V26, the scalar projection of b onto a is a· b (-1)(4) + 3(1) + 4(1) comp,b |a| 26 The vector projection is this scalar projection times the unit vector in the direction of a, below. proj,b = |a|

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
I was not able to finish this homework problem. Please help me solve it! Thank you.
Example
Video Example
Find the scalar projection and vector projection of b = (4, 1, 1) onto a = (-1, 3, 4).
Solution
Since Jal = V(-1)2 + 32 + 42 = V26, the scalar projection of b onto a is
%3D
a · b
(-1)(4) + 3(1) + 4(1)
compab
|al
V 26
The vector projection is this scalar projection times the unit vector in the direction of a, below.
a
projąb =
|a|
Transcribed Image Text:Example Video Example Find the scalar projection and vector projection of b = (4, 1, 1) onto a = (-1, 3, 4). Solution Since Jal = V(-1)2 + 32 + 42 = V26, the scalar projection of b onto a is %3D a · b (-1)(4) + 3(1) + 4(1) compab |al V 26 The vector projection is this scalar projection times the unit vector in the direction of a, below. a projąb = |a|
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning