### Vector Distance ProblemGiven the vectors:\[ \mathbf{u} = (2 + i, 0, 4 - 5i) \]\[ \mathbf{v} = (1 + i, 2 + i, 0) \]To find the distance between vectors \( \mathbf{u} \) and \( \mathbf{v} \):Select one of the following options:- \( \sqrt{47} \)- \( \sqrt{40} \)- \( \sqrt{45} \)- \( \sqrt{40} \)To solve this, you need to calculate the Euclidean distance between the two complex vectors, \(\mathbf{u}\) and \(\mathbf{v}\). The formula for the distance \( d \) between two vectors \( \mathbf{u} = (u_1, u_2, u_3) \) and \( \mathbf{v} = (v_1, v_2, v_3) \) is:\[ d = \sqrt{(u_1 - v_1)^2 + (u_2 - v_2)^2 + (u_3 - v_3)^2} \]First, compute the difference between corresponding components of each vector, then square each difference, sum them, and take the square root of the summation.This exercise enhances understanding of vector distances and applying the Euclidean distance formula in a complex vector space.

Two points in complex plane is given.

Answered: u = (2 + i, 0, 4- 5i) and v = (1 + i, 2…

u = (2 + i, 0, 4- 5i) and v = (1 + i, 2 + i, 0).

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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