SOLUTION: To the nearest tenth of a degree, find the angle formed by placing the vectors [4, 3] and [−7, 1] tail to tail.

You are given two vectors, u = (4,3) and v = (-7,1).

They want you find the angle 'a' between these two vectors.


Use the standard formula for the angle between two vectors

                (u,v)
    cos(a) = ----------- ,
              |u| * |v|

where (u,v) in the numerator is the scalar product of vectors u and v,

and |u|*|v| in the denominator is the product of the lengths of vectors u and v.


The scalar product of vectors u and v is  (u,v) = 4*(-7) + 3*1 = -28 + 3 = -25.


The length of vector u is  |u| =  =  = .

The length of vector v is  |v| =  =  = ,


So, cos(a) =  =  =  = .


Thus, angle 'a' is either 135° or 225°.


For further analysis, notice that vector 'u' is in first quadrant QI, while vector 'v' is in second quadrant (QII).


So, you conclude that the minimal angle 'a' is 135° precisely.    ANSWER