If A=i+2j, B=−2i+j, C=4i+3j , Find X And Y Such That C=xa+yb

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Question

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

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SolutionShow 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= 4and2x + y = 3Solving the above simultaneous equations, we have,x = 2 and y = -1

shaalaa.comVector and Cartesian Equations of a Line - Linear Combination of Vectors Report Error Is there an error in this question or solution?Q 1.2.5Q 1.2.4Q 2.1.12014-2015 (March)

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2014-2015 (March) (with solutions)Q 1.2.5 | 2 marks

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If`[ bara bar b barc ] ≠ 0 and barp = [ barb xx barc ]/([ bara bar b barc ]), barq = [ barc xx bara ]/([ bara bar b barc ]), barr = [ bara xx barb ]/[ bara bar b barc ]`

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