- #1

shwin

- 19

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I'm having trouble visualizing [tex]\ R^{4}[/itex](a domain of reals in four dimensions).

1. Describe a procedure in given 3 vectors, finds a fourth vector perpendicular to those three. Explain why we can use it in analogous fashion to the normal vector to a plane in [tex]\ R^{3}[/itex].

Here, I'm thinking taking the normal vector of each vector and then adding the three normals would be sufficient, but I am not sure how this is analogous to the normal vector to a plane in the xyz system.

2. How many vertices does the unit cube have in [tex]\ R^{n}[/itex] have? What is the furthest distance from the origin that one can be on the unit cube in [tex]\ R^{n}[/itex]? What is the average distance of the vertices to the origin?

First part I have [tex]\ 2^{n}[/itex], second part a square root of [ a summation from i = 1 to i = n of [tex]\ n^{2}[/itex]]

But the last part stumps me...average distance? and writing a formula for this is a bit confusing too.

1. Describe a procedure in given 3 vectors, finds a fourth vector perpendicular to those three. Explain why we can use it in analogous fashion to the normal vector to a plane in [tex]\ R^{3}[/itex].

Here, I'm thinking taking the normal vector of each vector and then adding the three normals would be sufficient, but I am not sure how this is analogous to the normal vector to a plane in the xyz system.

2. How many vertices does the unit cube have in [tex]\ R^{n}[/itex] have? What is the furthest distance from the origin that one can be on the unit cube in [tex]\ R^{n}[/itex]? What is the average distance of the vertices to the origin?

First part I have [tex]\ 2^{n}[/itex], second part a square root of [ a summation from i = 1 to i = n of [tex]\ n^{2}[/itex]]

But the last part stumps me...average distance? and writing a formula for this is a bit confusing too.

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