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Question

a=2^i+^j+^k,b=^i+5^jandc=4^i+4^j+2^k the projection of the vector 3a2b on the vector c is

A
11
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B
-11
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C
13
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D
none of these
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Solution

The correct option is D none of these
Given vectors,
a=2i+j+k
b=i+5j
c=4i+4j+2k
3a2b=3(2i+j+k)2(i+5j)
=6i+3j+3k2i10j
=8i7j+3k
Now unit vector along c will be given as
^c=c|c|=4^i+4^j+2^k42+42+22
46^i+46^j+26^k
=(3a2b)^.c
(8^i7^j+3^k).(46^i+46^j+26^k)
=8×467×46+3×26
=326286+66
=163143+1
=1614+33=273=9
Ans is (D) None of these

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