# If a=i+2j, b=−2i+j, c=4i+3j , find x and y such that c=xa+yb - Mathematics and Statistics

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

#### 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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