In Exercises 15-18, let R² have the Euclidean inner product. a. Find the orthogonal projection of u onto the line spanned by the vector v. b. Find the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. 15. и %3D (-1, 6); v %3D = () 16. u = (2, 3); v = 12 13' 13 5' 5

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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In Exercises 15–18, let R² have the Euclidean inner product.
a. Find the orthogonal projection of u onto the line spanned by
the vector v.
b. Find the component of u orthogonal to the line spanned by
the vector v, and confirm that this component is orthogonal
to the line.
15. и %3D (-1, 6); v %3D
) 16. u = (2, 3); v= ()
16. и 3D (2, 3); v 3
13' 13
17. u = (2, 3); v= (1,1)
18. и %3D (3, —1); v%3D (3,4)
Transcribed Image Text:In Exercises 15–18, let R² have the Euclidean inner product. a. Find the orthogonal projection of u onto the line spanned by the vector v. b. Find the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. 15. и %3D (-1, 6); v %3D ) 16. u = (2, 3); v= () 16. и 3D (2, 3); v 3 13' 13 17. u = (2, 3); v= (1,1) 18. и %3D (3, —1); v%3D (3,4)
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