If a̅, b̅ and c̅ are any three non-zero vectors, then ( a̅ + 2b̅ + c̅ ) · [(a̅ - b̅) × ( a̅ - b̅ - c̅ )] =

1
[ a̅ b̅ c̅ ]
2
2 [ a̅ b̅ c̅ ]
3
3 [ a̅ b̅ c̅ ]
4
4 [ a̅ b̅ c̅ ]

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