Show that the vectors:

A=2i-3j and B=-3i+4.5j are antiparallel.

here

A = 2i - 3j

and 

B = 3i + 4.5j

so, from dot product

A.B = |A||B|Cosθ

or the angle between them will be

Cosθ = A.B / |A||B|

so,

Cosθ = (2i - 3j).(3i + 4.5j) / √(13 x 29.5 ) = -19.5 / √(380.25)

or

Cosθ = -1

thus, angle θ = 180 deg. and the two vectors will be anti-parallel.