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Question 6: Explain vector product of two vectors.       


Definition of Vector or cross Product

A vector product of two vectors is one which yields a vector quantity.

×   = AB sinθ

If and are two vectors to be multiplied vectorally, then their resultant is a vector vecr.

The resultant vector is perpendicular to both  and   and its magnitude is equal to the product of the magnitudes of and   and the sine of the smaller angle between them. The direction of the resultant vector is determined by right hand rule.

This is important to note that unlike dot product, cross product is not commutative. The order of the vectors in the product is important.
 ×   ≠   × 

  Properties of Vector Product

Some of the important properties of the vector product are as follow.

  • Vector Product does not obey the Commutative Property.
    If  and   are two vectors then,
     ×   ≠   × 
  • Vector Product obeys the distributive property.
    If  ,and vecr  are three vectors, then
    vecr × (  ×  ) = ( vecr ×  ) +  ( vecr ×  )
  • If  ×   = 0, then either,
    1.  = 0
    2.  = 0
    3. both are zero
    4. Or the angle between them   is 0°

Physical significance of Vector Product

Vector product has key importance in the study of Physics. Important physical quantities are determined with the help of vector product.

  • Torque is determined with the help of vector product of and .
  • Angular momentum of a body is determined by vector product.
  • Area of a parallelogram is determined by the use of vector product. If   and   are the adjacent sides of a parallelogram and vecc  is its area, then

Apart from Mechanics, vector product is also used in other branches of Physics.


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