What is the angle between <5,8,2 > and < 4,6,-1 >?

1 Answer
Jun 26, 2016

Angle between vectors < 5, 8, 2 > and < 4, 6, -1 > is 28.682^o

Explanation:

The angle between vectors A=< a_1, a_2, a_3 > and B=< b_1, b_2, b_3 > is given by

A*B=|A||B|costheta, where A*B is the dot product and |A| and |B| are absolute value of the two vectors.

As A=< 5, 8, 2 > and B=< 4, 6, -1 >, hence

A*B=5*4+8*6+2*(-1)=20+48-2=66

|A|=sqrt(5^2+8^2+2^2)=sqrt(25+64+4)=sqrt93

|B|=sqrt(4^2+6^2+(-1)^2)=sqrt(16+36+1)=sqrt53

Hence costheta=66/(sqrt93xxsqrt53)=66/(9.64365xx7.28011)

= 66/75.231=0.8773

and theta=28.682^o