Calculate p- and n- by the formulas given above use step i

Question

Projection of a Vector onto Another Vector

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- onto the plane formed by P^- and N^- to get P^-₂ :

P^-₂ = Proj p^-(w^-) + Proj N^-(w^-)

 

Then N₂ is found by N₂ = w^- - P^-₂ . Use Step II of the Maple supplement to plot

2. u^- = (-4, 3, 5) v^-= (2, -1, 4) and w^- = (3,5, -4)

Provide a printout of your Maple plot: include both the blue output as well as the plot.