vector geometry

Question

Three non zero vectors a, b, c  are related as

c (vector) = 2 a (vector) and

b (vector) = - 5 c (vector) .

Then the angle between a (vector) and b (vector)  is 

 

 

 

a)   0 degrees

b)  45 degrees

c)   90 degrees

d)  180 degrees

Answer 1

                    a•b

cos(θ) = ----------------    and  a = (1/2)c   and   b = -5c

               ||a||·||b||

 

                         (1/2)c • (-5)c

so  θ = arccos(--------------------)

                      ||(1/2)c||·||-5c||

 

                        (-5/2) c•c

        = arccos(---------------)

                       (5/2) ||c||²

 

        = arccos(-1)