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Q.

If α→∥(β→×γ→), then (α→×β→)⋅(α→×γ→) equals to

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a

|α→|2(β→⋅γ→)

b

|β→|2(γ→⋅α→)

c

|γ→|2(α→⋅β→)

d

|α→||β→||γ→|

answer is A.

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Detailed Solution

α→∥(β→×γ→)⇒α→⊥β→ and α→⊥γ→ Now,  (α→×β→)⋅(α→×γ→) =|α→|2(β→⋅γ→)−(α→⋅β→)(α→⋅γ→) =|α→|2⋅(β→⋅γ→)
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