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What are dimension and basis of vector space of points found on line x=y/2=z/3?

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lightjazz | Student, Undergraduate | eNoter

Posted August 24, 2013 at 2:55 PM via web

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What are dimension and basis of vector space of points found on line x=y/2=z/3?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 24, 2013 at 5:30 PM (Answer #1)

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You need to consider the following relation, such that:

`x/1 = y/2 = z/3 = bar v => {(x = bar v),(y = 2bar v),(z = 3bar v):}`

Hence, you may consider the following vectors `(x,y,z) = (bar v,2bar v,3bar v) = bar v*(1,2,3)`

You should notice that giving values to bar v you may get the entire vector spece, including `bar v = 0` , hence, the vector `(1,2,3)` represent a basis for vector space, having the dimension 1.

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