1.

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

Answer»

`x=(4)/(7),y=(6)/(7)`
`x=(10)/(7),y=(4)/(7)`
`x=(8)/(7),y=(2)/(7)`
`x=2, y=3`

SOLUTION :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)`


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