Find the angle to the nearest degree between each pair of ve

Find the angle (to the nearest degree) between each pair of vectors. 11. (2, -3, (5, 2) 12. (3, -4), (4, 3) 13. (2, -3, 1), (4, -2, -3) 14. (2, 0, 5), (-5, -4, 2)

Solution

11) A=<2,-3>

B=<5,2>

A*B =10-6= 4

|A| =sqrt(4+9)=sqrt(13)

|B|= sqrt(25+4) =sqrt( 29)

theta =arc cos (4)/(sqrt(13*29)

theta = arc cos (0.2059)= 78 degrees

13) A= <2,-3,1>

B=< 4, -2, -3>

A*B = 8+6-3=14-3=11

|A|=sqrt( 10)

|B|= sqrt(29)

theta =arc cos( 0.5872)

=54 degrees