Q1Considering the vectors A = 6a, + 8a, + 24a, and B = 3ax + 4a, + 5a,; please answer thefollowing questions;а) А хВb) (В хА)-Вc) Explain your solutions in part (a) and (b) verbally with your own word, (i.e. write atleast couple of sentences to explain your solution for each part). Please use your ownwording and be explanatory.

Answered: Q1 Considering the vectors A = 6a, +…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.55P

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$\vec{A} = 6 \vec{a_{x}} + 8 \vec{a_{y}} + 24 \vec{a_{z}} \vec{B} = 3 \vec{a_{x}} + 4 \vec{a_{y}} + 5 \vec{a_{z}} ∵ \vec{A} \times \vec{B} = [\begin{matrix} \vec{a_{x}} & \vec{a_{y}} & \vec{a_{z}} \\ 6 & 8 & 24 \\ 3 & 4 & 5 \end{matrix}] \Rightarrow \vec{A} \times \vec{B} = [8 \times 5 - 4 \times 24] \vec{a_{x}} + [6 \times 5 - 3 \times 24] \vec{a_{y}} + [6 \times 4 - 3 \times 8] \vec{a_{z}} \Rightarrow \vec{A} \times \vec{B} = - 56 \vec{a_{x}} - 42 \vec{a_{y}}$

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$\vec{A} = 6 \vec{a_{x}} + 8 \vec{a_{y}} + 24 \vec{a_{z}} \vec{B} = 3 \vec{a_{x}} + 4 \vec{a_{y}} + 5 \vec{a_{z}} ∵ \vec{B} \times \vec{A} = [\begin{matrix} \vec{a_{x}} & \vec{a_{y}} & \vec{a_{z}} \\ 3 & 4 & 5 \\ 6 & 8 & 24 \end{matrix}] \Rightarrow \vec{B} \times \vec{A} = [4 \times 24 - 8 \times 5] \vec{a_{x}} + [3 \times 24 - 6 \times 5] \vec{a_{y}} + [3 \times 8 - 6 \times 4] \vec{a_{z}} \Rightarrow \vec{B} \times \vec{A} = 56 \vec{a_{x}} + 42 \vec{a_{y}} ∴ [\vec{B} \times \vec{A}] . \vec{B} = [56 \vec{a_{x}} + 42 \vec{a_{y}}] . [3 \vec{a_{x}} + 4 \vec{a_{y}} + 5 \vec{a_{z}}] \Rightarrow [\vec{B} \times \vec{A}] . \vec{B} = 56 \times 3 + 42 \times 4 + 0 [∵ \vec{a_{x}} . \vec{a_{x}} = 1 & \vec{a_{x}} . \vec{a_{y}} = 0] \Rightarrow [\vec{B} \times \vec{A}] . \vec{B} = 336$

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