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I have a problem on vector.

Vectors $ \vec a= (2, 4) ,\vec b = (−1, 2),$ and $\vec c = (c_1, c_2)$ all have the initial point at the origin, what are the coordinates of their terminal points?

Can you direct me on how to find terminal points for vector $\vec c$? Thanks. Aaron

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  • $\begingroup$ Vectors don’t have “initial” and “terminal” points—they have magnitude and direction. It’s line segments that have two points. $\endgroup$ – Chase Ryan Taylor Jun 12 at 16:27
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It works the same as with $\vec{a}$ and $\vec{b}$: the $x$-component of the vector tells you by how much you move on the $x$-axis, and the $y$-component tells you by how much you move on the $y$-axis. Since you start from the origin, that should tell you the answer.

If it doesn't, try with other examples of $c_1$ and $c_2$ and you'll see :)

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    $\begingroup$ I understand terminal points for a (2, 4) and b (-1, 2). But c I am not sure. Is it c (c1, ,c2)? Not sure this makes sense. $\endgroup$ – Lisa Levi Jun 12 at 15:45
  • $\begingroup$ Yes it is. For $\vec{a}$, you move $2$ units on the $x$-axis, and 4 on the $y$-axis. So you land on $(2,4)$. Same with $\vec{c}$: you move $c_1$ units on the $x$-axis and $c_2$ units on the right axis, so you land on $(c_1,c_2)$. $\endgroup$ – Arthur Jun 12 at 16:09
  • $\begingroup$ Because all 3 vectors start at origin, I tried to add vectors a and b to get c e.g. c (2-1, 4+2) -> c (1, 6). However, apparently this seems to be incorrect. Any advice? Thank you. $\endgroup$ – Lisa Levi Jun 12 at 16:48
  • $\begingroup$ Why would you think it is incorrect? Addition for vectors is indeed defined component-wise, you do have a + b = (1, 6) $\endgroup$ – Arthur Jun 12 at 17:04
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    $\begingroup$ Thank you very much. I got it. $\endgroup$ – Lisa Levi Jun 14 at 0:12

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