Given point pe R, and a direction 0, show that the line {p+ t : t...

Transcribed Image Text:

Given point pe R", and a direction 0, show that the line {p+ t : t R} is independent of the choice of p. i.e. If is another point of this line, then {p+ at : t R} = {+ t : t R}. Show the same thing if is replaced with a non-zero multiple of that. This problem shows that the equation of the line is not unique. We can prove similar thing about planes. (Hint. t is parameter, think about replacing it with s or something like that). Given point pe R", and a direction 0, show that the line {p+ t : t R} is independent of the choice of p. i.e. If is another point of this line, then {p+ at : t R} = {+ t : t R}. Show the same thing if is replaced with a non-zero multiple of that. This problem shows that the equation of the line is not unique. We can prove similar thing about planes. (Hint. t is parameter, think about replacing it with s or something like that).

Answer rating: 100% (QA)

Let q be another point on the line pat t R Then we can write q p sa for some s R Now lets show that ... View the full answer