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The volume of parallelopipe can be given by

The volume of parallelopipe can be given by Correct Answer Scalar triple product

Correct option-1

Concept:

The volume of a parallelopiped bounded by vectors A, B, and C can be obtained by (A × B) • C
If three vectors are coplanar then the volume of the parallelopiped bounded by these three vectors
should be zero or we can say that their scalar triple product should be zero.

Scalar triple product of vector A, B, and C is written by-
A • (B × C) is called scalar triple product. It is a scalar quantity.

We can show that A •(B × C) = (A × B) •C = B•(C × A).

Explanation:

The scalar triple product is one of the concepts in vectorial algebra important,

because its absolute value |(a×b)⋅c| is the volume of the parallelepiped spanned by a, b, and c

(i.e., the parallelepiped whose coterminous sides are the vectors a, b, and c).

The volume of the parallelepiped formed with coterminous vectors a, b, and c is given by
Volume = area of base⋅height

Volume = ∥a × b∥ ∥c∥ |cosϕ| = |(a × b)⋅c|.
The formula results from properties of the cross product:

The area of the parallelogram base is ∥a × b∥ and the vector a×b is perpendicular to the base.

The height of the parallelepiped is ∥c∥ |cosϕ|.

Scalar or Dot Product
The scalar or dot product of two vectors A and B is denoted by A • B and is read as A dot B.
It is defined as the product of the magnitudes of the two vectors A and B and
the cosine of their included angle θ.
Thus, A • B = AB cosθ (a scalar quantity)

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