Answer to Question #232924 in Physics for Eshiii

Question #232924
Given two vectors A= 4.00i + 3.00j and B= 5.00i− 2.00j, b) write an expression for the vector difference A-C using unit vector; d) In a vector diagram show A,B, and A-B, , and also show that your diagram agrees qualitatively with your answer in part (c). e) A × B. f) A ∙ B
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Expert's answer
2021-09-04T15:19:41-0400

Given:

A=4.00i+3.00j{\bf A}= 4.00{\bf i} + 3.00{\bf j}

B=5.00i2.00j{\bf B}= 5.00{\bf i} -2.00{\bf j}


(b)

C=AB=(4.00i+3.00j)(5.00i2.00j)=1.00i+5.00j{\bf C}={\bf A}-{\bf B}\\= (4.00{\bf i} + 3.00{\bf j})-( 5.00{\bf i} -2.00{\bf j})\\= -1.00{\bf i} +5.00{\bf j}

(d)



(e)

A×B=(4.00i+3.00j)×(5.00i2.00j)=23.0k{\bf A}\times{\bf B}=(4.00{\bf i} + 3.00{\bf j})\times (5.00{\bf i} -2.00{\bf j})\\ =-23.0{\bf k}

(f)

AB=(4.00i+3.00j)(5.00i2.00j)=14{\bf A}\cdot{\bf B}=(4.00{\bf i} + 3.00{\bf j})\cdot (5.00{\bf i} -2.00{\bf j})=14


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