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Question

If α=2^i+3^j^k,β=^i+2^j4^k,γ=^i+^j+^k then (α×β).(α×γ)=

A
60
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B
64
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C
74
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D
74
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Solution

The correct option is D 74
=¯α.(¯βׯαׯγ)
=¯α.((¯β.¯γ)¯α(¯β.¯α)¯γ)
=|¯α|2(¯β.¯γ)(¯α.¯γ)(¯β.¯α)
=(14)(3)(4)(8)
=74

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