If A, B, C and D are the points with position vectors `hati-hatj+hatk,2hati-hatj+3hatk,2hati-3hatkand3hati-2hatj+hatk` respectively, then find the projection of `vec(AB)andvec(CD)`.

Explanation

Here, `vec(OA)=hati+hatj-hatk,vec(OB)=2hati-hatj+3hatk,vec(OC)=2hati-3hatkandvec(OD)=3hati-2hatj+hatk`
`:.vec(AB)=vec(OB)-vec(OA)=(2-1)hati+(-1-1)hatj+(3+1)hatk`
`=hati-2hatj+4hatk`
and `vec(CD)=vec(OD)-vec(OC)=(3-2)hati+(-2-0)hatj+(1+3)hatk`
`=hati-2hatj+4hatk`
So, the projection of `vec(AB)" along "vec(CD)=vec(AB).vec(CD)/(|vec(CD)|)`
`=((hati-2hatj+4hatk).(hati-2hatj+4hatk))/(sqrt(1^(2)+2^(2)+4^(2)))`
`(1+4+16)/(sqrt21)=(21)/(sqrt21)`
`sqrt21` units