HW_1_Solutions

HW_1_Solutions - EEE 241 Solution to Assignment #1 P.2-1...

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EEE 241 Solution to Assignment #1 P.2-1 Given three vectors as follows, A = ˆ a x + ˆ a y 2 ˆ a z 3 , B = ˆ a y 4 + ˆ a z , C = ˆ a x 5 ˆ a z 2 , Fnd (a) ˆ a A (c) A · B (e) the component of A in the direction of C (g) A · ( B × C ) and ( A × B ) · C Solution: (a) ˆ a A = A A = 1 14 a x + ˆ a y 2 ˆ a z 3) (c) A · B = (ˆ a x + ˆ a y 2 ˆ a z 3) · ( ˆ a y 4 + ˆ a z ) = 11 (e) the component of A in the direction of C is given by A · ˆ a C ˆ a C = C C = 1 29 a x 5 ˆ a z 2) A · ˆ a C = (ˆ a x + ˆ a y 2 ˆ a z 3) · 1 29 a x 5 ˆ a z 2) = 11 29 (g) A · ( B × C ) = (ˆ a x + ˆ a y 2 ˆ a z 3) · [( ˆ a y 4 + ˆ a z ) × a x 5 ˆ a z 2)] = (ˆ a x + ˆ a y 2 ˆ a z 3) · a x 8 + ˆ a y 5 + ˆ a z 20) = 42 ( A × B ) · C = [(ˆ a x + ˆ a y 2 ˆ a z 3) × ( ˆ a y 4 + ˆ a z )] · a x 5 ˆ a z 2) = ( ˆ a x 10 ˆ a y ˆ a z 4) · a x 5 ˆ a z 2) = 42 P.2-2 Given, A = ˆ a x ˆ a y 2 + ˆ a z 3 , B = ˆ a x + ˆ a y ˆ a z 2 , 1
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fnd the expression For a unit vector C
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HW_1_Solutions - EEE 241 Solution to Assignment #1 P.2-1...

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