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If the sum of vectors v and w as shown in the image above is (5,1) and the difference is (1,5). Can we fill the entire xy plane usimg combinations of v and w?

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  • $\begingroup$ Did you manage to make any progress? For example, could you find $\bf v$ and $\bf w$? $\endgroup$ – Minus One-Twelfth Mar 14 at 9:25
  • $\begingroup$ I have not made any progress. What would help me is if I could see a general formula for finding v and w. I am totally new to linear algebra $\endgroup$ – Adam Mar 14 at 9:28
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    $\begingroup$ Here's a hint: imagine from usual algebra if you knew $a+b$ and $a-b$, could you work out the values of $a$ and $b$ (for example if $a+b=100$ and $a-b=10$, can you find what $a$ and $b$ are)? Pretty much same method would work here for finding $\bf v$ and $\bf w$. $\endgroup$ – Minus One-Twelfth Mar 14 at 9:29
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    $\begingroup$ Correct! $\color{grey}\,$ $\endgroup$ – Minus One-Twelfth Mar 14 at 9:58
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    $\begingroup$ To divide a vector by a number, simply divide each component by that number. Once you know what $\bf v$ and $\bf w$ are, you should know how to find the angle between them using dot products (if not, it would be best to revise how to do so). $\endgroup$ – Minus One-Twelfth Mar 14 at 10:21

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