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Given the vectors M = -10ax +4ay-8a- and N = 8ax + 7ay-2a-, find: a) a unit vector in the direction of -M + 2N. - - -M+2N = 10ax − 4ay +8a₂ +16ax + 14ay − 4a, = (26, 10, 4) Thus a (26, 10, 4) |(26, 10, 4)| = (0.92, 0.36, 0.14) b) the magnitude of 5ax +N-3M: (5, 0, 0)+(8,7,-2)-(-30, 12, -24)= (43, -5, 22), and (43, -5, 22)| = 48.6. c) |M|2N|(M+N):

Given the vectors M = -10ax +4ay-8a- and N = 8ax + 7ay-2a-, find: a) a unit vector in the direction of -M + 2N. - - -M+2N = 10ax − 4ay +8a₂ +16ax + 14ay − 4a, = (26, 10, 4) Thus a (26, 10, 4) |(26, 10, 4)| = (0.92, 0.36, 0.14) b) the magnitude of 5ax +N-3M: (5, 0, 0)+(8,7,-2)-(-30, 12, -24)= (43, -5, 22), and (43, -5, 22)| = 48.6. c) |M|2N|(M+N):

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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(Electromagnetic field) Hello sir I want a detailed solution for this solution
1- Given the vectors M = -10ax +4ay-8a- and N = 8ax + 7ay-2a-, find: a) a unit vector in the direction of -M + 2N. -M + 2N = 10ax - 4ay+8a₂ +16a, + 14ay -4a₂ = (26, 10, 4) Thus 2- a= (26, 10, 4) |(26, 10, 4)| b) the magnitude of 5ax +N-3M: (5, 0, 0)+(8, 7, -2)-(-30, 12, -24) =(43, -5, 22), and (43, -5,22)| = 48.6. = (0.92, 0.36, 0.14) c) |M||2N| (M+N): |(-10, 4, -8)||(16, 14, −4)|(−2, 11, -10) = (13.4)(21.6)(-2, 11, -10) = (-580.5, 3193, -2902) Given three points, A(4, 3, 2), B(-2, 0, 5), and C(7, -2, 1): a) Specify the vector A extending from the origin to the point A. mn= A = (4, 3, 2) = 4ax +3ay + 2a₂ b) Give a unit vector extending from the origin to the midpoint of line AB. The vector from the origin to the midpoint is given by M = (1/2)(A + B) = (1/2) (4 − 2, 3 +0,2+5) = (1, 1.5, 3.5) The unit vector will be (1, 1.5, 3.5) |(1, 1.5, 3.5)| (0.25, 0.38, 0.89) c) Calculate the length of the perimeter of triangle ABC: Begin with AB= (-6, -3, 3), BC = (9, -2,-4), CA = (3, -5, -1). Then |AB|+|BC|+|CA| = 7.35 + 10.05 +5.91 = 23.32
Transcribed Image Text:1- Given the vectors M = -10ax +4ay-8a- and N = 8ax + 7ay-2a-, find: a) a unit vector in the direction of -M + 2N. -M + 2N = 10ax - 4ay+8a₂ +16a, + 14ay -4a₂ = (26, 10, 4) Thus 2- a= (26, 10, 4) |(26, 10, 4)| b) the magnitude of 5ax +N-3M: (5, 0, 0)+(8, 7, -2)-(-30, 12, -24) =(43, -5, 22), and (43, -5,22)| = 48.6. = (0.92, 0.36, 0.14) c) |M||2N| (M+N): |(-10, 4, -8)||(16, 14, −4)|(−2, 11, -10) = (13.4)(21.6)(-2, 11, -10) = (-580.5, 3193, -2902) Given three points, A(4, 3, 2), B(-2, 0, 5), and C(7, -2, 1): a) Specify the vector A extending from the origin to the point A. mn= A = (4, 3, 2) = 4ax +3ay + 2a₂ b) Give a unit vector extending from the origin to the midpoint of line AB. The vector from the origin to the midpoint is given by M = (1/2)(A + B) = (1/2) (4 − 2, 3 +0,2+5) = (1, 1.5, 3.5) The unit vector will be (1, 1.5, 3.5) |(1, 1.5, 3.5)| (0.25, 0.38, 0.89) c) Calculate the length of the perimeter of triangle ABC: Begin with AB= (-6, -3, 3), BC = (9, -2,-4), CA = (3, -5, -1). Then |AB|+|BC|+|CA| = 7.35 + 10.05 +5.91 = 23.32
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