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The multiplication of two vector quantities gives

The multiplication of two vector quantities gives Correct Answer either 1 or 2

Concept:

Vector Quantities

  • A physical quantity that requires magnitude and a particular direction, when it is expressed
  • Vector quantity must obey the rule of vector algebra.
  • Ex. Displacement, velocity, acceleration, force, etc.
  • A vector is represented by an arrow geometrically.
  • Its length is proportional to its magnitude.


In vector algebra, we usually have four basic operations-

1. Addition of vectors

  • Parallelogram laws
  • Triangle laws &
  • Polygon laws

2. Subtraction of vectors

3. Multiplication of vectors.

  • Scalar or Dot product.
  • Vector or Cross product.

4. Multiplication of vector with a scalar.

Explanation

  • The product of two vectors may give you either scalar or vector quantity.
  • It depends upon the operation through which it has obtained.
  • In the case of the dot product of two vectors, it always gives you a scalar quantity. That's why it is also called the scalar product.
  • While in the case of the vector or cross product, the result we obtain is a vector quantity.

Hence, option-3 is correct.

Product of Two Vectors
The product of two vectors is of two  kinds
(i) scalar or dot product.
(ii) Vector or a cross product.

(i) 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)

(ii) Vector or Cross Product
The cross product of two vectors A and B is denoted by A × B and read as A cross B.
It is defined as a third vector C whose magnitude is equal to the product of the
magnitudes of the two vectors A and B and the sine of their included angle θ.
Thus, if C = A × B, then C = AB sinθ.
The vector C is normal to the plane of A and B and points in the direction in which a right-handed screw would advance when rotated about an axis
perpendicular to the plane of the two vectors in the direction from A to B through the smaller angle θ between them or alternatively.

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