Problem Set (3D) For the following pair of vectors, Calculate 'P and 'N by the formulas given above. Use Step I of the Maple supplement to plot your results and to check your calculations. Provide a printout of your Maple plot: include both the blue output as well as the plot.
1. 'u = (- 4 , 3,5) and 'v =(2,-1,4)
Problem Set (Gram-Schmidt Orthogonalization) We are given the same vectors, 'u , 'v, 'P and 'N as in problem #1, above. Project the vector 'w Cv onto the plane formed by P and 'N to get 'P2 :
'P2 = Projp ( 'w) + ProjN( 'w)
Then 'N2 is found by 'N2 = 'w - 'P2. Use Step II of the Maple supplement to plot
your results and to check your calculations. Provide a printout of your Maple plot: include both the blue output as well as the plot.
2. 'u =(- 4, 3,5) , 'v=(2,-1,4) and 'w = (3,5, -4)