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Question

Why cross product is a vector quantity ?


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Solution

Dot product

  1. A dot product or scalar product is the product of two vectors.
  2. The resultant of the dot product is a scalar.
  3. If A and B are two two, their dot product is given by A·B. It has only magnitude.
  4. A·B=ABcosθ.

Cross product

  1. A Cross product or vector product is the product of two vectors.
  2. The resultant of the cross product is a vector perpendicular to the plane of the two vectors.
  3. Since the resultant is a vector hence it has both magnitude and direction.
  4. Therefore the cross product is a vector.
  5. If A and B are two vectors, their cross product is given by A×B. It has both magnitude and direction.
  6. A×B=ABsinθ.

From the above information, it is clear that cross-product is always a vector quantity.


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