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Question
A vector of magnitude 18 which is perpendicular to both the vectors 4^i−^j+3^k and −2^i+^j−2^k is
A vector of magnitude 18 which is perpendicular to both the vectors 4^i−^j+3^k and −2^i+^j−2^k is
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Solution
The correct option is B −6^i+12^j+12^k
The two vectors are,
→a=4^i−^j+3^k
→b=−2^i+^j−2^k
→c=→a×→b=−^i+2^j+2^k
The unit vector, ^c=→c|→c|=−^i+2^j+2^k√1+22+22=−^i+2^j+2^k3}
Therefore the required vector =18^c=18×−^i+2^j+2^k3=−6^i+12^j+12^k
The two vectors are,
→a=4^i−^j+3^k
→b=−2^i+^j−2^k
→c=→a×→b=−^i+2^j+2^k
The unit vector, ^c=→c|→c|=−^i+2^j+2^k√1+22+22=−^i+2^j+2^k3}
Therefore the required vector =18^c=18×−^i+2^j+2^k3=−6^i+12^j+12^k
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