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Question

If a,b and c are three mutually orthogonal unit vectors, then the triple product [a+b+ca+bb+c] is equal to

A
0
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B
1 or 1
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C
6
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D
3
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Solution

The correct option is C 6
[a+b+ca+bb+c] = {axb+c) +bx(b+c)+cx(b+c)}(a+b) + {ax(a+b) + bx(a+b) + cx(a+b)}(b+c)
After simplification we get,
=a(a×b)+a(a×c)+b(a×b)+b(a×c)+b(c×a)+b(c×b)+c(c×a)+c(c×b)
since a, band c are orthonal unit vectors, a×c=|a||b|sin90o and so on
=a2b+a2c+ab2+cb2a+ac2+bc2
substituting the value of 1 for the unit vectors, we get,
=6

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