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Question

Find the projection of (a+2b) on c where a=2^i2^j+^k,b=^i+2^j2^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 621
Given, a=2^i2^j+^k,b=^i+2^j2^k and c=2^i^j+4^k
We need to find the projection of (a+2b) on c
We know that the projection of (a+2b) on c is given by (a+2b).^c, where ^c is the unit vector of c.
So, we have
^c=c|c|=2^i^j+4^k22+(1)2+42=121(2^i^j+4^k)
Also, (a+2b)=(2^i2^j+^k)+2(^i+2^j2^k)
(a+2b)=4^i+2^j3^k
Hence, projection is given by
(a+2b).^c=(4^i+2^j3^k).(121(2^i^j+4^k))
821221=621

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