Given A = 4i + 3j and B = -2i + 5j :

a) Find the magnitude and direction (measured from the x-axis) of A,B, and A - 3B .

b) Give, in unit vector notation, a vector C such that C = A but C does not equal A.

Solution:

a) A = [ (4)² + (3)²]^1/2 = 5.0

tan^-1 = 3/4

= 36.9

B = [ (-2)² + (5)²]^1/2 = 5.39

tan^-1 = 5/(-2)

= -68.2   but that is in the wrong quadrant, thus we want = -68.2 + 180 = 111.8

A - 3B   =  (4+6)i + (3-15)j   =   10i -12j so the magnitude of A - 3B is

= [ (10)² + (-12)²]^1/2 = 15.6

tan^-1 = (-12)/10

= -50.2

b) We can choose any vector with the same magnitude (length) but that points in a different direction (there are an infinite number of them!). Examples include

C = 4i - 3j,   C = -4i + 3j,   C = 5i, etc...

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