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Question

Let a=2^i+3^j6^k, b=2^i3^j+6^k and c=2^i+3^j+6^k. Let a1 be the projection of a on b and a2 be the projection of a1 on  c. Then, a1.b is equal to
  1. 41
  2. 287
  3. 41
  4. 417


Solution

The correct option is C 41
a1=[(2^i+3^j6^k)(2^i3^j+6^k)7](2^i3^j+6^k)7
a1=4149(2^i3^j+6^k)

a2=4149[(2^i3^j+6^k)(2^i+3^j+6^k)7](2^i+3^j+6^k)7

a2=41(49)2(49+36)(2^i+3^j+6^k)

a2=943(49)2(2^i3^j6^k)

a1b=4149(2^i3^j+6^k)(2^i3^j+6^k)=41

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