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

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.