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ps://i.stack.imgur.com/xVD0O.png

Why does $a+b+c = a-a+c$? I don't understand. Is it some math property that i didn't know of?

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    $\begingroup$ just susbtitute $b=-a$ $\endgroup$ Jan 29 at 12:06
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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Jan 29 at 12:11
  • $\begingroup$ Presumably an earlier part of the question told you about $ABC$ $\endgroup$
    – Henry
    Jan 29 at 12:19

2 Answers 2

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Note that we have $a+b=0$, so $b=-a$. Using that, we have $a+b+c=a-a+c$.

In general, $a+b+c=a-a+c$ is not true. It is true only if we know $b=-a$.

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From second inner product : $$\begin {pmatrix} a & b & c \end{pmatrix} . \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = a.1+b.1+c.0$$

As the above two vectors are orthogonal then $a+b=0$

So substitute $b=-a$ in the equation which you mentioned.

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