Find the angle a in radians between the vectors and a Soluti

Find the angle a in radians between the vectors and a

Solution

let us say first vector is \'v\' and second is \'u\' , the angle between them is \'a\'

then cos a = v.u/|v|.|u|

v.u is a cross proudct of the vectors (just multiply the corresponding values)

v.u= (-5).(2) + (-4) (-1) + (4).(3)

v.u= -10 +4 +12

v.u = 6

|v|= sqrt(5^2 +4^2 +4^2) = sqrt(25+16+16)

|v| =sqrt(47)

|u|=sqrt(4 +1+9) =sqrt(14)

cosa = 6/sqrt(47).sqrt(14)

cosa=0.212

a =1.36 radians