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Question

Let a=^i^k, b=x^i+^j+(1x)^k and c=y^i+x^j+(1+xy)^k, then [a,b,c] depends on

A
Only 4y
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B
Only x
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C
Both x and y
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D
Neither x nor y
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Solution

The correct option is C Neither x nor y
Given
a=^i^k
b=x^i+^j+(1x)^k
c=y^i+x^j+(1+xy)^k
We have [abc]=a.(b×c)

Now,
b×c=∣ ∣ ∣^i^j^kx11xyx1+xy∣ ∣ ∣

=^i(1+xxx2)^j(x+x2xyy+xy)+^k(x2y)a(b×c)=1
Which does not depend on x and y

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