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Linear Algebra: Hyperplanes

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The equation 2x_1 + 2x_2 - 3x_3 + 8x_4 = 6 defines a hyperplane in R^4.
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.

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Solution Summary

In this solution, hyperplanes are investigated. The solution is detailed and well presented in an attached Word document.

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Proof:
We can rewrite the equation of the hyperplane as .
a. The normal vector of the hyperplane is , which is the coefficients of the equation.
b. The distance between the origin and the hyperplane is

c. Now we make a ...

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