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(μ2−1)−1(μ−1)+1(1−μ)=0 ⇒μ3−μ−μ+1+1−μ=0 ⇒μ3−3μ+2=0 ⇒(μ−1)(μ2+μ−2)=0 ⇒(μ−1)(μ−1)(μ+2)=0 ⇒μ=1,1,−2 So, distinct real values of μ are 1 and −2. Therefore, thier sum =−1