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I have two vectors $\vec{A}(2.735, -4.737)$ and $\vec{B}(2.735, 4.737)$, and a vector $\vec{P}(1.380, -0.796)$ in between these two vectors. When I calculate the angle between $\vec{A}$ and $\vec{B}$ it is $120$ degrees. However, the angle between $\vec{A}$ and $\vec P$ is $ 60$ degrees and that of $\vec P$ and $\vec B$ is $90$ degrees. So the sum of individual angles $(150)$ is greater than the total angle. Why is this anomaly? Here is a plot of the three vectors $\vec A,\vec B$ and $\vec P$

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  • $\begingroup$ Please include more information about your problem, i.e. how got these values. $\endgroup$
    – DjPatpat
    Mar 9, 2023 at 11:38
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    $\begingroup$ The angle between $\vec{A}$ and $\vec{P}$ is (approximately) $30°.$ $\endgroup$
    – aqualubix
    Mar 9, 2023 at 11:43
  • $\begingroup$ This could happen in 3D; it's the triangle inequality in spherical geometry. $\endgroup$
    – mr_e_man
    Mar 9, 2023 at 15:11

1 Answer 1

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The angle between $\vec{A}$ and $\vec{P}$ is $$\begin{align}\arccos\left(\frac{\vec{A}\cdot\vec{P}}{\left\|\vec{A}\right\|\left\|\vec{P}\right\|}\right)&=\arccos\left(\frac{2.735\cdot1.38+(-4.737)(-0.796)}{\sqrt{2.735^2+(-4.737)^2}\sqrt{1.38^2+(-0.796)^2}}\right)\\ &=\arccos(0.86583\ldots)\\ &=30^\circ\end{align}$$ so you just made a calculation error.

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