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Show that vector{a.(b x c)} is equal in magnitude to the volume of a parallelopiped formed on the three vectors vector(a,b and c).

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In Fig. A parallelopiped is formed by the three vectors

vector(OA = a),

vector(OB = b),

And vector(OC = c)

Now, vector(b x c) = |vector b| |vector c| sin 90° n

= |vector b| |vector c| n

Where n is a unit vector along vector OA and is perpendicular to the plane containing vector (b and c)

There vector{a.(b x c)} = vector{a |b| |c|} n

= vector{(|a|)(|b|)(|c|)} cos 0°

= vector{|a| |b| |c|}

which is equal in magnitude to the volume of the parallelopiped.

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