Questions:
Linear Algebra: Hyperplanes
The equation 2x1 + 2x2 - 3x3 + 8x4 = 6 defines a hyperplane in R4.
a. Give its normal vector a.
b. Find its distance from the origin using dot products.
c. Find the point on the hyperplane closest to the origin by using the parametric equation of the line through 0 with direction vector a.
Double-check your answer in b.
d. Find the distance from the point w = (1, 1, 1, 1) to the hyperplane using dot products.
e. Find the point on the hyperplane closest to w by using the parametric equations of the line through w with direction vector a. Double-check your answer in d.