question_answer

Given that the vectors \[\vec{a}\] and \[\overrightarrow{b}\] are non collinear, the values of x and y for which the vector equality \[2\,\,\vec{u}-\vec{v}=\vec{w}\] holds true if \[\vec{u}-x\,\vec{a}=2y\vec{b},\]\[\vec{v}=-\,2y\vec{a}+3x\vec{b},\] \[\vec{w}=4\vec{a}-2\vec{b}\]are-

A) \[\text{ }x=\frac{4}{7},\,\,\,y=\frac{6}{7}\]

B) \[x=\frac{10}{7},\,\,\,y=\frac{4}{7}\]

C) \[x=\frac{8}{7},\,\,\,y=\frac{2}{7}\]

D) \[x=2,\,\,\,y=3\]