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Question

If a and b are vectors in space given by a=^i2^j5 and b=2^i+^j+3^k14, then the value of

(2a+b).[(a×b)×(a2b)] is

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is C 5
p×(q×r)=(p.r)q(p.q)r

(q×r)×p=(p.r)q+(p.q)r

Hence,

E=(2a+b).[2|b|2a2(ab)b(ab)a+|a|2b]
ab=2270=0

|a|=1

|b|=1

ab=0

E=(2a+b).[2|b|2a+|a|2b]

=4|a|2|b|2+|a|2(a.b)+2|b|2(ba)+|a|2|b|2

=5|a|2|b|2=5

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