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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|

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
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...
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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|
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