Question

Given three vectors A = 24i + 33j, B = 55i - 12j and C = 2i + 43j

 (a) Find the magnitude of each vector.

 (b) Write an expression for the vector difference A - C.

 (c) Find the magnitude and direction of the vector difference A-B.

 (d) In a vector diagram show vector A + B, and A - B, and also show that your diagram agrees 

Answer 1

a)

$$A=\sqrt{24^2+33^2}=41\\B=\sqrt{55^2+12^2}=56\\C=\sqrt{2^2+43^2}=43\\$$

b)

$$\bold{A-C}=(24-2,33-43)=(22,-10)$$

c)

$$\bold{A-B}=(24-55,33-(-12))=(-31,45)$$

$$|A-B|=\sqrt{31^2+45^2}=55$$

$$\theta=90-\arctan{\frac{45}{31}}=125\degree$$

d)