Calculating an angle between 2 vectors given their value and the value of their sum

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Given the value of 2 vectors A and B, and the value of the resultant vector C, how would I go about calculating the angle between A and B?

Thanks a lot

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2 Answers

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By value, I assume you mean magnitude and direction. Thus, you should be able to calculate the angle between them: $\theta_a = cos^{-1}(\frac{\vec{A}_x}{\vec{A}})$ and $\theta_b = cos^{-1}(\frac{\vec{B}_x}{\vec{B}})$. Now perform subtraction on $\theta_a$ and $\theta_b$, and find its absolute value.

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As $A,B,C$ are the sides of a triangle, you can just apply e.g. the law of cosines

$$C^2=A^2+B^2-2AB\cos(\gamma)$$ and solve for $\gamma$. Then the angle between them is obviously the supplement angle $\phi = \pi-\gamma$.

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