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Question

# I: If →a=3^i−2^j+^k, →b=2^i−4^j−3^k, →c=−^i+2^j+2^k then →a+→b+→c=4^i−4^jII: If →a=^i−^j+2^k,→b=2^i+3^j+^k,→c=^i−^k, then magnitude of →a+2→b−3→c is √78

A
Only I is true
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B
Only II is true
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C
Both I and II are true
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D
Neither l nor ll are true
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Solution

## The correct option is C Both I and II are trueConsider Statement I→a+→b+→c=(3i−2j+k)+(2i−4j−3k)+(−i+2j+2k)=(3+2−1)i+(−2−4+2)j+(1−3+2)k=4i−4jHence statement 1 is true.Consider Statement 2→a+2→b−3→c=(i−j+2k)+(4i+6j+2k)−(3i−3k)=(1+4−3)i+(−1+6)j+(2+2+3)k=2i+5j+7k|2i+5j+7k|=√4+25+49=√78Hence statement 2 is true.

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