Cross Products Determinants of Matrices        The 3 X 3 arrays below will return the components for the cross product of two vectors. Most programmable calculators have a MATRIX mode or setting that can accomodate the arrays and evaluate the determinants of matrices.        Enter the values as shown, and solve the determinant of the matrix. The direction numbers or components x , y , and z of the resultant vector are returned. To program an Excel worksheet, create a 3 X 3 group of cells and apply the MDETERM function.        The upper row is the only row that changes. Note that the values represent the direction numbers of the unit vectors i , j , and k . The next two rows are the direction numbers of vectors a and b , as outlined in the definitions of Vector Products .        The definition of direction numbers or components includes direction cosines, values based on trig functions of the angles SS , DD , and R1 as described in Vector Components (go back to the LINEAR ALGEBRA page), or appropriate dimensions from the Hip/Valley roof. HOME PAGE