    Question

# Find the projection of (→a+2→b) on →c where →a=2^i−2^j+^k,→b=^i+2^j−2^k and →c=2^i−^j+4^k

A
821
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B
821
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C
621
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D
621
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Solution

## The correct option is D −6√21Given, →a=2^i−2^j+^k,→b=^i+2^j−2^k and →c=2^i−^j+4^k We need to find the projection of (→a+2→b) on →c We know that the projection of (→a+2→b) on →c is given by (→a+2→b).^c, where ^c is the unit vector of →c. So, we have ^c=→c|→c|=2^i−^j+4^k√22+(−1)2+42=1√21(2^i−^j+4^k) Also, (→a+2→b)=(2^i−2^j+^k)+2(^i+2^j−2^k) ⇒ (→a+2→b)=4^i+2^j−3^k Hence, projection is given by (→a+2→b).^c=(4^i+2^j−3^k).(1√21(2^i−^j+4^k)) ⇒ 8−2−12√21=−6√21  Suggest Corrections  1      Similar questions
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