Show that a.(b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.
Consider a parallelepiped with origin O and sides a, b, and C as shown in the below figure,
If 
is unit vector which is perpendicular to both vectors b and c then direction of a and 
be same.
Therefore, cross product
= bc 
(∵ θ = 900)
∴ a.(
) = abc 
= abc (∵ angle between bc 
and a is 00)
Hence, a.(
) = Volume of the parallelepiped
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