Answer to Question #132983 in Field Theory for Aliha

Question

Given three vector A=24i+33j, b=55 -12j and c=2i+43j

a) find magnitude of each vector

b) write an expression and direction of the vector difference A-B

d)in a vector diagram show A+B and A-B and also show the diagram agrees

Answer 1

(a)

$$|{\bf A}|=\sqrt{24^2+33^2}=40.8$$

$$|{\bf B}|=\sqrt{55^2+12^2}=56.3$$

$$|{\bf C}|=\sqrt{2^2+43^2}=43.05$$

(b)

$${\bf A}-{\bf B}=(24{\bf i}+33{\bf j})-(2{\bf i}+43{\bf j})=22{\bf i}-10{\bf j}$$

$$\theta=\tan^{-1}\frac{-10}{22}=-24^{\circ}$$

(d)

$${\bf A}+{\bf B}=(24{\bf i}+33{\bf j})+(2{\bf i}+43{\bf j})=26{\bf i}+76{\bf j}$$

$$\theta=\tan^{-1}\frac{76}{26}=71^{\circ}$$