Given that the vectors `alpha` and `beta` are non-collinear. The values of `x` and `y` for which `vecu - vecv = vecw` holds true if `vecu = 2 xalpha + ybeta, vec v = 2yalpha + 3xbeta` and `vecw = 2alpha - 5 beta` are

Options

A. `x=2, y=1`
B. `x=1, y=2`
C. `x=-2, y=1`
D. `x=-2, y=-1`

Answer

A

Explanation

`ve(u)-vec(v)=vec(w)`
`(2x vec(alpha)+y vec(beta))-(2y vec(alpha)+3xvec(beta))=2vec(alpha)-5vec(beta)`
`(2x-2y)vec(alpha)+(y-3x)vec(beta)=2vec(alpha)-5vec(beta)`
`:. 2x-2y=2 ...(i)`
and `3x-y=5 ...(ii)`
Solving equation (i) and (ii) , we get
x=2 and y=1
`:. ` Option(a) is correct.