Given that A=3a_x +5a_y -7a_z and B=a_x -2a_y +a_x , find: (a)|2B+0.4A|, (b) A*B-|B|^2 , (C) Atimes B

Bernard Boyer 2022-07-25 Answered
Given that A = 3 a x + 5 a y 7 a z   a n d   B = a x 2 a y + a z , find:
( a ) | 2 B + 0.4 A | , ( b ) A B | B | 2 , ( c ) A × B
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Answers (1)

Vartavk
Answered 2022-07-26 Author has 11 answers
(a)
12B + 0.4A = <12*1+0.4*3,12*(-2)+0.4*5 , 12*1+0.4*(-7)>
=< 13.2 , 22 , 9.2 >= 13.2 a x 22 a y + 9.2 a z
b)
A.B = 3*1 + 5*(-2) + (-7)*1 = 3-10-7 =-14
| B | 2 = 1 2 + ( 2 ) 2 + 1 2 = 1 + 4 + 1 = 6
A . B | B | 2 = 14 6 = 20
c)
A × B = | i j k 3 5 7 1 2 1 | = ( 5 14 ) i + ( 7 3 ) j + ( 6 5 ) k
= 9 i 10 j 11 k

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