If ` vec aa n d vec b` are two given vectors and `k` is any scalar, then find the vector ` vec r` satisfying ` vec rxx vec a+k vec r= vec bdot`

Explanation

`vecrxxveca+kvecr=vecb`
`or (vecrxxveca)xxveca+kvecrxxveca= vecbxxveca`
`or (vecr. veca)veca-(veca.veca)vecr+k(vecb-kvecr)=vecbxxveca`
`or (vecr. veca)veca+kvecb-vecbxxveca=(|veca|^(2)+k^(2))vecr`
`or vecr((vecr.veca)veca+kvecb-vecbxxveca)/(|veca|^(2)+k^(2))`
Also, in Eq, (i) taking dot product with `veca`., we have
`(vecrxxveca).veca+kvecr.veca=vecb.veca`
`or vecr. veca=(vecb.veca)/k`
`Rightarrow vecr=1/(k^(2)+|veca|^(2))[((veca.vecb)veca)/k+kvecb+(vecaxxvecb)]`