Let `vec a=hat i+hat j+hat k and vec b=i and vec c=c_1 hat i + hat c_2 j +c_3 hat k` Then (a) if `c_1 = 1 and c_2=2` , find `c_3` which makes ` vec a , vec b, vec c ` coplanar (b) if `c_2 = -1 and c_3= 1` , show that no value of `c_3` can makes ` vec a , vec b, vec c ` coplanar.

Explanation

`[vec{a}, vec{b} ,vec{c} =0]`


`|[1,1,1] ,[1,0,0] ,[c_{1},-1,1]|=0 `


`(0)-1(1-0)+1(-1)=0 `


`-1-1=0 `


`-2=0`


Which is not true.


`Rightarrow vec{a}, vec{b}, vec{c} `are not coplanar for any value of `c_{1}.`