__Question 7.5__:**a**. (

**b**×

**c**) is equal in magnitude to the volume of the parallelepiped formed on the three vectors,

**a**,

**b**and

**c**.

__Solution__:A parallelepiped with origin O and sides

*a*,

*b*, and

*c*is shown in the following figure.

Volume
of the given parallelepiped =

Let

∴

= bc

a.(b X c) = a(bc

= abc Cosθ

= abc Cos 0

= abc

= Volume of the parallelepiped

*abc***OC = a***OB = b***OC = c**Let

**n^**be a unit vector perpendicular to both*and***b***. Hence,***c****n^**and*have the same direction.***a**∴

**b X c**= bc Sin θ**n^**= bc

**n^**a.(b X c) = a(bc

**n^**)= abc Cosθ

**n^**= abc Cos 0

= abc

= Volume of the parallelepiped

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