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, +…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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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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