calculus properties of cross products?

2 Answers

• use the distributive properties of the cross product:

  (j – k) x (k – i) = (j-k) x k – (j-k) x i =

  j x k – k x k – ( j x i – k x i ) = j x k – k x k – j x i + k x i

  Now k x k = 0

  The other 3 you can do by visualizing it geometrically: draw them out and use the right hand rule for the direction. The length of the vector that results in each of these three must = 1 since the norm of a x b is |a||b|sinΘ, and in all these 3 cases we have |i|=|j|=|k| = 1 and Θ= pi/2 so sin Θ = 1. :

  j x k = i

  j x i = – k

  k x i = j

  So we get i – (-k) + j = i + j + k

• Cross Products Property