If `a ,\ b ,\ c` are non zero non coplanar vectors, prove that the following vectors are coplanar. `5 vec a+6 vec b+7 vec c ,\ 7 vec a-8 vec b+9 vec c\ a n d\ 3 vec a+20 vec b+5 vec c`

Explanation

Let us take:


`vec P=5 vec a+6 vec b+7 vec c `


`vec Q=7 vec a-8 vec b+9 vec c`


`vec R= 3 vec a+20 vec b+5 vec c`


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

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


Therefore,


`3 vec a+20 vec b+5 vec c=alpha(5 vec a+6 vec b+7 vec c)+ beta (7 vec a-8 vec b+9 vec c)`


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