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.