Let ` vec a , vec ba n d vec c ,` be non-zero non-coplanar vectors. Prove that: ` vec a-2 vec b+3 vec c ,-2 vec a+3 vec b-4 vec c \ a n d \ vec c-3 vec b+5 vec c` are coplanar vectors. `2 vec a- vec b+3 vec c , vec a+ vec b-2 vec c \ a n d \ vec a+ vec b-3 vec c` are non-coplanar vectors.

Explanation

For `(i)`


Let us take:


`vec P=vec a-2 vec b+3 vec c `


`vec Q=-2 vec a+3 vec b-4 vec c`


`vec R=vec a-3 vec b+5 vec c`


As we have to show them as coplanar so there must be a relation like this

`vec P= alpha vec Q+ beta vec R`


Therefore,


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