Given that the vectors `vec(a) and vec(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)= - 2 y vec (a) + 3 x vec(b), vec(w) = 4 vec(a)-2 vec(b) ` areA. `x=(4)/(7), y= (6)/(7)`B. `x=(10)/(7), y= (4)/(7)`C. `x=(8)/(7), y= (2)/(7)`D. `x=2, y= 3`

Given that the vectors `vec(a) and vec(b)` are non- collinear, the val

1.	Given that the vectors `vec(a) and vec(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)= - 2 y vec (a) + 3 x vec(b), vec(w) = 4 vec(a)-2 vec(b) ` areA. `x=(4)/(7), y= (6)/(7)`B. `x=(10)/(7), y= (4)/(7)`C. `x=(8)/(7), y= (2)/(7)`D. `x=2, y= 3`
Answer» Correct Answer - B We have, `2 vec(u) - vec(v) = vec(w)` `rArr (2x+2y-4)vec(a)+(-3x+4y+2)vec(b) =0` `rArr 2x+2y-4=0 and -3x+4y+2=0[ because vec(a) vec(b) " are non- collinear "]` `rArr x=10//7, y=4//7.`

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