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Question

The set of values of m for which the vectors ^i+^j+m^k,^i+^j+(m+1)^k and (^i^j+m^k) are non-coplanar

A
R
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B
R1
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C
R2
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D
ϕ
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Solution

The correct option is A R
Let a=^i+^j+m^k,b=^i+^j+(m+1)^k & c=(^i^j+m^k)

Thus [abc]=∣ ∣11111m+111m∣ ∣
=∣ ∣01101m+121m∣ ∣,C1C1C2

=2(m+1m)=2
Hence a,b,c are always non-coplaner for any values of m

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