CrossProduct.md (896B)
1 # Cross Product 2 3 Khan 4 5 **Definition:** The cross product of two vectors is the vector orthogonal to them. 6 7 The cross product is only defined in R^3. 8 9 ### Calculation 10 11 To calculate the cross product we simply do the following: 12 13 a = [a_1, a_2, a_3] 14 b = [b_1, b_2, b_3] 15 16 o = [a_2b_3 - a_3b_2 , a_3b_1 - a_1b_3 , a_1b_2 - a_2b_1] 17 18 Conceptually, we take the determinant of the bottom two rows then reverse determinent of top and bottom rows then deteminent of top two rows. 19 20 The length of the cross product is the distance the second vector is projected onto the first vector multiplied by the length of the first vector. This is pretty much the inversion of the dot product's value where we find the projected distance of the second multiplied by the distance of the first. 21 22 The cross product's length is 0 if both vectors are colinear. Conversely, it is maximized when the vectors are orthogonal.