HSC Science (General) 12th Board ExamMaharashtra State Board
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# Solution for If a=i+2j, b=−2i+j, c=4i+3j , find x and y such that c=xa+yb - HSC Science (General) 12th Board Exam - Mathematics and Statistics

ConceptVectors Linear Combination of Vectors

#### Question

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

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 1.2.5 | 2.00 marks

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Solution for question: If a=i+2j, b=−2i+j, c=4i+3j , find x and y such that c=xa+yb concept: Vectors - Linear Combination of Vectors. For the courses HSC Science (General) , HSC Arts, HSC Science (Computer Science), HSC Science (Electronics)
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