A=2a_x + a_y -3a_z B=a_y -a_z C=3a_x +5a_y +7a_z determine: (a) A-2B+C (b)C-4(A+B) (c) (2A-3B)/(|C|)

tamkieuqf

tamkieuqf

Answered question

2022-08-05

A = 2 a x + a y 3 a z
B = a y a z
C = 3 a x + 5 a y + 7 a z
determine:
(a)A-2B+C
(b)C-4(A+B)
(c) 2 A 3 B | C |

Answer & Explanation

Nicholas Mathis

Nicholas Mathis

Beginner2022-08-06Added 12 answers

(a) A 2 B + C = 2 a x + a y 3 a z 2 ( a y a z ) + 3 a x + 5 a y + 7 a z
= 5 a x + 4 a y + 6 a z
(b) C 4 ( A + B ) = 3 a x + 5 a y + 7 a z 4 ( 2 a x + a y 3 a z + a y a z )
= 5 a x 3 a y + 23 a z
(c) ( 2 A 3 B ) / | C | = ( 2 ( 2 a x + a y 3 a z ) 3 ( a y a z ) ) / 2
= ( 4 / 2 ) a x ( 1 / 2 ) a y ( 3 / 2 ) a z
Marco Hudson

Marco Hudson

Beginner2022-08-07Added 5 answers

A =< 2 a x , a y , 3 a z >
B =< 0 a x , a y , a z >
C =< 3 a x , 5 a y , 7 a z >
just add and subtract like components.
A-2B+C=
< 2 a x , a y , 3 a z > 2 < 0 , a y , a z > + < 3 a x , 5 a y , 7 a z >
=< 5 a x , 4 a y , 6 a z >
C-4(A+B)=
< 3 a x , 5 a y , 7 a z > 4 ( < 2 a x , a y , 3 a z > + < 3 a x , 5 a y , 7 a z > )
=< 3 a x , 5 a y , 7 a z > 4 < 5 a x , 6 a y , 4 a z >
=< 17 a x , 19 a y , 9 a z >
2 A 3 B | C | =
1 ( 3 a x ) 2 + ( 5 a y ) 2 + ( 7 a z ) 2 ( 2 < 2 a x , a y , 3 a z > 3 < 3 a x , 5 a y , 7 a z > )
= < 5 a x , 13 a y , 27 a z > ( 3 a x ) 2 + ( 5 a y ) 2 + ( 7 a z ) 2

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