Find the vector →r which is perpendicular to →a=^i−2^j+5^k and →b=2^i+3^j−^k and →r.(2^i+^j+^k)+8=0
A
→r=−13^i−11^j+7^k
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B
→r=13^i−7^j+11^k
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C
→r=−13^i+11^j+7^k
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D
→r=13^i+7^j+11^k
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Solution
The correct option is C→r=−13^i+11^j+7^k Vector perpendicular to →a=^i−2^j+5^k and →b=2^i+3^j−^k is →a×→b=−13^i+11^j+7^k Let →r=t(−13^i+11^j+7^k) but →r.(2^i+^j+^k)=−8 ⇒−26t+11t+7t=−8 ⇒t=−1 ∴→r=−13^i+11^j+7^k Hence, option C.