If `veca=-hati+hatj+hatk andvecb=2hati+0hatj+hatk` then find vector `vecc` satisfying the following conditions, (i) that it is coplaner with `veca and vecb` , (ii) that it is `bot` to `vecb` and (iii) that `veca.vecc=7`.

Explanation

`Let vecc = x x hati + y hatj+zhatk`
then from conditon (i).
`|{:(x,y,z),(-1,1,1),(2,0,1):}|=0 or x+3y-2z=0`
from condition (ii),
2x+z=0
from condition (iii),
-x+y+z=7
solving (i),(ii) and (iii) we get the values of x,y and z , hence vector `vecc,1/2(-3hati+5hatj+6hatk)`