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Question
The orthogonal projection of 3^i+2^j−5^k on a vector perpendicular to 2^i−^j+2^k is
The orthogonal projection of 3^i+2^j−5^k on a vector perpendicular to 2^i−^j+2^k is
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Solution
The correct option is A 133^i+43^j−113^k
Orthogonal projection =3^i+2^j−5^k−(3^i+2^j−5^k).(2^i−^j+2^k)4+1+4(2^i−^j+^k)
=(3^i+2^j−5^k)−6−2−109(2^i−^j+2^k)=(3^i+2^j−5^k)+23(2^i−^j+2^k)=13^i+4^j−11^k3
Orthogonal projection =3^i+2^j−5^k−(3^i+2^j−5^k).(2^i−^j+2^k)4+1+4(2^i−^j+^k)
=(3^i+2^j−5^k)−6−2−109(2^i−^j+2^k)=(3^i+2^j−5^k)+23(2^i−^j+2^k)=13^i+4^j−11^k3
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