Given that the vectors a and b are non-collinear, the values of x and y for which the vector equality 2u - v = w holds true if
u = xa + 2y b, v = - 2y a + 3xb, w = 4a - 2b are

Options

A. `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

B

Explanation

We have, 2u - v = w
`implies 2(xa+2yb)-(-2ya+3xb)=4a-2b`
`implies (2x+2y-4)a+(-3x+4y+2)b=0`
`implies 2x+2y-4=0 and -3x+4y+2=0` [`because` a, b are non-collinear]
`x=(10)/(7), y=(4)/(7)`