Cross product of two vectors Assignment Help

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Cross product of two vectors: 

The vector product of 2 vectors 645_Addition of two vectors9.png and 1499_Addition of two vectors10.png, denoted by 645_Addition of two vectors9.pngx1499_Addition of two vectors10.png, can be defined as the vector |645_Addition of two vectors9.png| sinθ, where θ is the angle between vectors 645_Addition of two vectors9.png and 1499_Addition of two vectors10.pngand 41_Cross product of two vectors7.png is a unit vector perpendicular to both 645_Addition of two vectors9.png and 1499_Addition of two vectors10.png(that is, perpendicular to the plane of 645_Addition of two vectors9.png and 1499_Addition of two vectors10.png).The sense of 41_Cross product of two vectors7.png can be obtained by the right hand thumb rule that is 645_Addition of two vectors9.png1499_Addition of two vectors10.png and 41_Cross product of two vectors7.png form a right-handed screw.

    2076_Cross product of two vectors.png

If we curl fingers of our right hand from 645_Addition of two vectors9.png to 1499_Addition of two vectors10.pngthrough smaller angle (keeping the initial point of 645_Addition of two vectors9.png and 1499_Addition of two vectors10.pngsame), the thumb points in direction of 41_Cross product of two vectors7.png. In this case, 645_Addition of two vectors9.png,1499_Addition of two vectors10.pngand 41_Cross product of two vectors7.png (or 645_Addition of two vectors9.pngx1499_Addition of two vectors10.png), in that order are said to form a right handed system. It is obvious that |645_Addition of two vectors9.pngx1499_Addition of two vectors10.png|= absinθ.

Properties:

  • 820_Cross product of two vectors1.png
  • Any vector perpendicular to the plane of  1085_Cross product of two vectors6.png is a real number. Unit vector perpendicular to  1274_Cross product of two vectors2.png
  • 2021_Cross product of two vectors5.png denotes the area of the parallelogram OACB, whereas area of  2433_Cross product of two vectors3.png

Area is treated as a vector with the direction in proper sense.

557_Cross product of two vectors4.png

 

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