Find the cosine of the angle between A and B with respect to

Find the cosine of the angle between A and B with respect to the standard inner product on M₂₂.

Carry out all calculations exactly and round to 4 decimal places the final answer only.

cos ? =

Solution

Let a = (4,3,1,-1) and b = (4,3,3,0) . Then a.b = 16+9+3= 28 . Also a.b = |a||b| cos, where is the angle between A and B. Further,  |a| = ( 16+9+1+1) =27 and |b| = ( 16+9+9) = 34 . Therefore, (27)(34 )cos = 28. Thus, cos = 28/(27)(34 ) = 28/(918). Hence = arccos(28/(918)