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in this video were going to talk about how to find the cross product of two vectors so lets say if vector a is 3i plus 5j minus 7k and vector b is 2i minus 6j plus 4k so what is the cross product of vectors a and b how can we find the answer what id like to do is first put this in the form of a matrix this is i j k which corresponds to the x y and z components of a vector and then first we need to put vector a in the middle because that comes first so its going to be 3 5 and negative 7. and then vector b which is 2 negative 6 and 4. and basically you got to find the determinant of this 3x3 matrix so its going to equal i i is found in row 1 column 1 and its going to leave behind a 2 by two matrix highlighted in that red box so thats five negative seven negative six and four and then its going to be minus j now j is in the first row second column so we have left over 3 2 and negative 7 4. next we have positive k and k is in the first row third column which leaves behind three fiv
