Q5 of 33 Page 178

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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