Vectors

• tags:Math

• Cross product

  • The vector product of two vectors A,B is given by AxB, and the resultant vector is perpendicular to both A and B. The product of their magnitude gives the area of the polygon which is the magnitude of the resultant vector. Its a 3-dimensional vector with the direction given by the right-hand rule, with the thumb giving the direction of the resultant.
  • 

  • A × B =

    A

    B

    sin θ

The vecotrs a and b form a parallelogram and the area of the parallelogram is the base time height The heigh is given by the sin of the angle between vectors = asin(angle) - The cross product of perpendicular vectors is the same as the product of magnitude as sin90 is 1. The cross product of parallel vectors is zero. - AxB != BxA as it flips the direction of the resultant vector. - - We know that the standard basis vectors i, j, and k satisfy the below-given equalities. i × j = k and j × i = –k j × k = i and k × j = –i k × i = j and i × k = –j Also, the anti-commutativity of the cross product and the distinct absence of linear independence of these vectors signifies that: i × i = j × j = k × k = 0 - -

• Vectors