1
Question
Find a vector perpendicular to each of the vectors →a+→b and →a−→b, where →a=∧i+∧j+∧k,→b=∧i+2∧j+3∧k.
Find a vector perpendicular to each of the vectors →a+→b and →a−→b, where →a=∧i+∧j+∧k,→b=∧i+2∧j+3∧k.
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Solution
The correct option is D None of these
→a+→b=2^i+3^j+4^k→a−→b=0^i−^j−2^k(→a+→b)×(→a−→b)=∣∣
∣
∣∣^i^j^k2340−1−2∣∣
∣
∣∣=i(−6+4)−^j(−4)+^k(−2)=−2^i+4^j−2^k=2(−^i+2^j−^k)
Therefore a vector perpendicular to each of the vectors →a+→b and →a−→b is −^i+2^j−^k
Hence the option D (None of these) is the correct answer.
→a+→b=2^i+3^j+4^k→a−→b=0^i−^j−2^k(→a+→b)×(→a−→b)=∣∣
∣
∣∣^i^j^k2340−1−2∣∣
∣
∣∣=i(−6+4)−^j(−4)+^k(−2)=−2^i+4^j−2^k=2(−^i+2^j−^k)
Therefore a vector perpendicular to each of the vectors →a+→b and →a−→b is −^i+2^j−^k
Hence the option D (None of these) is the correct answer.
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