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Question

Find the value of k1 and k2 for which V can be represented as V = k1A+k2B. Where, V=2ij ,
A = 3i2j and B = 3i+3j.

A
k1=1 and k2=1
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B
k1=35 and k2=12
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C
k1=23 and k2=25
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D
k1=35 and k2=115
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Solution

The correct option is D k1=35 and k2=115
The vector V can be expressed asV=k1A+k2B
2ij = k1(3i2j) + k2(3i+3j)
2ij = (3k1+3k2)i + (2k1+3k2)j
Equating terms from both sides
2 = (3k1+3k2)
1 = (2k1+3k2)
Solving both the equations we get
k1 = 35 and k2 =115

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