If ` vec a ,\ vec b ,\ vec c` are three vectors such that ` vec adot\ vec b= vec adot\ vec c` and ` vec a\ x\ vec b= vec a\ x\ vec c ,\ vec a\ !=0` , then show that ` vec b= vec c` .

Explanation

`veca.vecb=veca.vecc`


`veca.vecb−veca.vecc=0`


`veca.(vecb−vecc)=0`


`abs(veca.vecb−vecc)` `cosθ=0`


`veca=0 also cosθ=0`


`veca.vecb=veca.vecc=0`


`abs(vecb−vecc)=0`


`:.vecb=vecc`