Answer to Question #232924 in Physics for Eshiii

Question

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

Answer 1

Given:

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

${\bf B}= 5.00{\bf i} -2.00{\bf j}$

(b)

$${\bf C}={\bf A}-{\bf B}\\= (4.00{\bf i} + 3.00{\bf j})-( 5.00{\bf i} -2.00{\bf j})\\= -1.00{\bf i} +5.00{\bf j}$$

(d)

(e)

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

(f)

$${\bf A}\cdot{\bf B}=(4.00{\bf i} + 3.00{\bf j})\cdot (5.00{\bf i} -2.00{\bf j})=14$$