This question comes from the material you covered independently in chapter 3. Consider the vectors u = (1, 3, 0, 7), v = (2, 1, 0, -1) and w = (-1, 0, 1, 3) in R4 under the usual vector addition and scalar multiplication. Find the following for these three given vectors. Show work neatly, step by step, to support your answers. (Be mindful of order of operations). a. Find: ||v + u +w|| b. Find: (v - u) • w (this is dot product -- please excuse the big fact dot symbol)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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This question comes from the material you covered independently in chapter 3.

Consider the vectors **u** = (1, 3, 0, 7), **v** = (2, 1, 0, -1) and **w** = (-1, 0, 1, 3) in ℝ⁴ under the usual vector addition and scalar multiplication. Find the following for these three given vectors. Show work neatly, step by step, to support your answers. (Be mindful of order of operations).

a. Find: \( ||v + u + w|| \)

b. Find: \( (v - u) \cdot w \)  (this is dot product -- please excuse the big fact dot symbol)
Transcribed Image Text:This question comes from the material you covered independently in chapter 3. Consider the vectors **u** = (1, 3, 0, 7), **v** = (2, 1, 0, -1) and **w** = (-1, 0, 1, 3) in ℝ⁴ under the usual vector addition and scalar multiplication. Find the following for these three given vectors. Show work neatly, step by step, to support your answers. (Be mindful of order of operations). a. Find: \( ||v + u + w|| \) b. Find: \( (v - u) \cdot w \) (this is dot product -- please excuse the big fact dot symbol)
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