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Question

If α||(β×γ), then (α×β).(α×γ) equals to

A
|α|2(β.γ)
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B
|β|2(γ.α)
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C
|γ|2(α.β)
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D
|α||β||γ|
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Solution

The correct option is A |α|2(β.γ)
α(β×γ)
α is perpendicular to both β and γ
(α×γ)=|α||γ|ˆβ
(α×β)=|α||β|ˆγ
(α×γ).(α×β)=|α||γ|ˆβ.|α||β|ˆγ=|α|2|β||γ|ˆβ.ˆγ=|α|2β.γ


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