Verified answer

cos theta = u v / ||u| |v||

u v = (-5)(2)+(-5)(-2)+(-5)(1) = -10+10-5 = -5

||u|| = sqrt((-5)^2+(-5)^2+(-5)^2 ) = sqrt(25+25+25) = sqrt(75)

||v|| = sqrt(2^2+(-2)^2+1^2)) = sqrt(4+4+1) = sqrt(9)=3

cos theta = -5 / (sqrt(75) * 3) =0.19245

theta = cos^-1(0.19245) = 1.7644 radians

= (1.7644)*(180/pi) = 101.09 degrees

a.b = -5, |a| = 5√3, and |b| = 3

The angle between these vectors is arccos( -5 / ( 5√3 × 3 ) ) = arccos(-1/(3√3)) which is about 1.7644546 radians.