How to calculate a cross product | Matrix-determinant cross product | Cyclic Cross Product

Calculating the cross product of two arbitrary vectors isn’t exactly easy to do with the magnitude formula absin(theta) and the right hand rule. Instead, we need more exact mathematical methods to do it. This video covers two such methods. The first method is the matrix-determinant method, in which the two vectors are put in the second and third rows (respectively) of a 3x3 matrix. The first row is filled with the unit vectors x hat, y hat, and z hat. Take the determinant of this matrix, and you get the cross product! The second method is a method based on the Right-hand rule. Here, you treat the vectors as polynomials, and foil out or multiply the individual components of each vector. To determine the directions of the cross products of the unit vectors in your expansion (ie x hat x z hat, etc.), you can use the right hand rule or use the cyclic shortcut. The cyclic shortcut assembles x hat, y hat, and z hat in a sort of cycle and tells you that if you take the cross product of any two of the vectors in the direction of the cycle, you’ll get the third, “unused” unit vector in the positive direction. If you take the cross product of any two of the vectors opposite the direction of the cycle, you’ll get the third, “unused” unit vector in the negative direction. 0:00 The why 0:56 Matrix - Determinant Method 3:00 Calculating a Determinant 6:03 Example with Matrix Determinant Method 10:15 Cyclic Right Hand Rule Method 14:41 Example with Cyclic RHR Method 18:51 Outro