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Vector Diagram I answered this question correctly but am really struggling to find out how I did it?

What I thought I had to do was to count the length and width of the arrows for the letters it asks to add up.

Once I get these 2 values from each letter I use -tan(c/j) However after trying this I caunt seem to get the correct answer again. Would appriciate some help as to where im going wrong or if im on the right track at all.

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2 Answers 2

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The sum is ${-1 \choose -2}$. The resultant angle is the angle that the vector makes with respect to the $x$-axis. This will be an angle in the range $[0^\circ, 90^\circ]$. All that matters are the lengths of the sides relative to the angle $\theta$. No minus signs! Lengths are non negative. In this case $\tan \theta = \dfrac 21 = 2$. So $\theta = \arctan 2 \approx 63^\circ$

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The resultant should be ${3 \choose 1} + {-4 \choose -3} = {-1 \choose -2}$.

What you are doing is not correct. You should use the inverse tangent in this case: since $\tan \theta = \frac{-2}{-1}$ (opposite over adjacent), $\theta = \tan^{-1} \frac{-2}{-1} = 63.4º$.


If you don't like to use negatives, the vector has the same resultant as ${1 \choose 2}$, which also gives the same answer.

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  • $\begingroup$ why are the numbers negative? $\endgroup$
    – JakeeYm
    Sep 6, 2019 at 13:37
  • $\begingroup$ Sorry we need to back track further, i dont understand how your getting the initial values. What am I counting and what am I adding up? $\endgroup$
    – JakeeYm
    Sep 6, 2019 at 13:43
  • $\begingroup$ $C = {3 \choose 1}$ and $J = {-4 \choose -3}$ right? Then you are adding up the $x$-components and $y$-components separately: $3+(-4)=-1$, $1+(-3) = (-2)$. $\endgroup$
    – Toby Mak
    Sep 6, 2019 at 13:45

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