Find the cosine of the angle between the vectors with respec

Find the cosine of the angle between the vectors with respect to the standard inner product on P₂.

p = -1 + 3 x + 4 x² and q = 3 + 2x - 3x².

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

cos =

Solution

We have p.q = (-1)(3)+(3)(2)+(4)(-3) = -3+6-12= -9. Also, p.q = |p||q|cos where is the angle between the vectors p and q with respect to the standard inner product on P₂. Further, |p|= [(-1)² + 3² +4² ] = 26 and |q|= [ 3² +2²+(-3)² ] = (9+4+9) = 22. Therefore, (26)( 22) cos = -9. Hence cos = -9/(26*22) = -9/[2143]