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Question

The sum of the distinct real values of μ, for which the vectors, μ^i+^j+^k,^i+μ^j+^k,^i+^j+μ^k are co-planar, is:

A
0
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B
1
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C
1
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D
2
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Solution

The correct option is B 1
If the three vecors are coplanar, then ∣ ∣ ∣μ111μ111μ∣ ∣ ∣=0
μ(μ21)1(μ1)+1(1μ)=0
μ3μμ+1+1μ=0
μ33μ+2=0
(μ1)(μ2+μ2)=0
(μ1)(μ1)(μ+2)=0
μ=1,1,2
So, distinct real values of μ are 1 and 2.
Therefore, thier sum =1

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