If `a\ a n d\ b` ar non collinear vector such that `x_1 vec a+y_1 vec b=x_2 vec a+y_2 vec b` , then prove that `x_1=x_2a n d\ y_1=y_2dot`

Explanation

`x_{1} \vec{a}+y_{1} \vec{b}`=`\(x_{2} \vec{a}+y_{2} \vec{b})`


If a and b are non coll. vector


`(x_{1}-x_{2}) \vec{a}+(y_{1}-y_{2}) \vec{b}`=0


`(x_{1})-(x_{2})`=`0` `(y_{1})-(y_{2})`=`0`



`(x_{1})=(x_{2})` `(y_{1})=(y_{2})`