0

Let $v_1$ and $v_2$ be given vectors. $v = t_1v_1 + t_2v_2$ varies over the plane determined by the two vectors. The plane is parameterized by $t_1$ and $t_2$. Let $v_0$ be another given vector. What does $v = v_0 + t_1v_1 + t_2v_2$ parameterize?

I'd say that would be a plane since $v_0$ is a single non-scaled vector. Is that right?

godlessliburul
  • 35

1 Answers1

0

Imagine the whole plane being moved by the vector $v_0$. What then do you get?

user67953840
  • 693
  • Can you elaborate on the movement, please. I don't understand how or why $v_0$ moves the whole plane. – godlessliburul Jan 23 '15 at 13:37
  • By movement, I meant translation. – user67953840 Jan 23 '15 at 13:41
  • For example, let $v=[1 \quad 1]$ and $v_0=[0 \quad 2]$. Vector $v$ can be viewed as moving from the the origin to the point $(1,1)$. Can you imagine what $v_0$ will do if it is added to $v$? – user67953840 Jan 23 '15 at 13:47
  • $v + v_0$ is the point $(1, 3)$. Is the original plane centered(?) at the origin? The way I imagine it is that $v = t_1v_1 + t_2v_2$ describes the plane completely, so $v_0$ is redundant and has no effect. – godlessliburul Jan 23 '15 at 13:53
  • "... so $v_0$ is redundant and has no effect" - That's correct!

    That's what I meant when I said $v_0$ "moves" the plane. Any movement will still result to the same plane.

     – user67953840 Jan 23 '15 at 14:00