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Given v = 31 - 5) and w=i-j, a. Find projw v. b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. a. proj, v =D(Type your answer in terms of i and j.)

Given v = 31 - 5) and w=i-j, a. Find projw v. b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. a. proj, v =D(Type your answer in terms of i and j.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 13E
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Find Projwv using the Example and Decompose v into two vectors v1 and v2​, where v1 is parallel to w and v2 is orthogonal to w.

Given v = 3i - 5j and w=i-j, a. Find projw v. b. Decompose v into two vectors 1 and V2, where v, is parallel to w and v2 is orthogonal to w. ..... a. projw v = (Type your answer in terms of i and j.) (1,1) More Help me solve this View an example Get more help - Clear all Check answer
Transcribed Image Text:Given v = 3i - 5j and w=i-j, a. Find projw v. b. Decompose v into two vectors 1 and V2, where v, is parallel to w and v2 is orthogonal to w. ..... a. projw v = (Type your answer in terms of i and j.) (1,1) More Help me solve this View an example Get more help - Clear all Check answer
View an example | All parts showing Given v = 5i + 4j and w=i-j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. || " || To use the formula to find proj„v, we must find the dot product of v and w. V•w = (5)(1) + (4)(– 1) = 1 Now find the magnitude of w. Iw| = Jn} +(-13 %D %3D The denominator of the formula for projwv has the magnitude of w, squared. |w|? = (/2)? %D = 2 Using the formula, find proj,v. projwv v•W -w 1 - j) %3D - 1 1 -i- 2 b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. Close II
Transcribed Image Text:View an example | All parts showing Given v = 5i + 4j and w=i-j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. || " || To use the formula to find proj„v, we must find the dot product of v and w. V•w = (5)(1) + (4)(– 1) = 1 Now find the magnitude of w. Iw| = Jn} +(-13 %D %3D The denominator of the formula for projwv has the magnitude of w, squared. |w|? = (/2)? %D = 2 Using the formula, find proj,v. projwv v•W -w 1 - j) %3D - 1 1 -i- 2 b. Decompose v into two vectors v, and v2, where v, is parallel to w and v2 is orthogonal to w. Close II
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