If `vec(a)=-hat(i)+hat(j)+hat(k)` and `vec(b)=2hat(i)+0hat(j)+hat(k)` , then find vector `vec(c)` satisfying the following conditions : (i) that it is coplanar with `vec(a)` and `vec(b)` ,(ii) that it is `_|_` to `vec(b)`and (iii) that `vec(a)*vec(c)=7`.

Answer

`vec(c )=(1)/(2)(-3hati+5hatj+6hatk)`