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If `bara=bari+2barj, barb=-2bari+barj,barc=4bari+3barj`, find x and y such that `barc=xbara+ybarb`

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#### Solution

Given that `veca = hati +2hatj, vecb = −2hati +hatj, vecc = 4hati + 3hatj`

We need to find x and y such that `vecc = xveca + yvecb`

Substituting the values of a, b and c, in ` vec c = xveca + yvecb`, we have,

`4hati + 3hatj = x(hat i +2hatj )+ y (-2hati +hatj)`

`4hati + 3hatj = (x -2y)hat i + (2x + y) hatj`

Comparing the coefficients of i and j on both the sides, we have,

x-2y= 4

and

2x + y = 3

Solving the above simultaneous equations, we have,

x = 2 and y = -1

Concept: Vector and Cartesian Equations of a Line - Linear Combination of Vectors

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