Find the sine of the angle between the vectors `veca=3hati+hatj+2hatkandvecb=2hati-2hatj+4hatk`

Explanation

Here, `a_(1)=3,a_(2)=1,a_(3)=2andb_(1)=2,b_(2)=-2,b_(3)=4`
We know that,
`costheta=(a_(1)b_(1)+b_(2)b_(2)+a_(3)b_(3))/(sqrt(a_(1)^(2)+a_(2)^(2)+a_(3)^(3))sqrt(b_(1)^(2)+b_(2)^(2)+b_(3)^(3)))`
`=(3xx2+1xx(-2)+2xx4)/(sqrt(3^(2)+1^(2)+2^(2))sqrt(2^(2)+(-2)^(2)+4^(2)))`
`=(6-2+8)/(sqrt(14)sqrt(24))=(12)/(2sqrt(14)sqrt(6))=(6)/sqrt(84)=(6)/(2sqrt21)=(3)/sqrt(21)`
`:.sintheta=sqrt(1-cos^(2)theta)`
`=sqrt(1-(9)/(21))=sqrt((12)/(21))=(2sqrt3)/(sqrt3sqrt7)=(2)/(sqrt7)`