If vectors overrightarrow P, overrightarrow Q | vedclass

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$\cos^{-1}(\frac{12}{13})$

Vedclass · Answer

(C) Given magnitudes are $|\overrightarrow P| = 5$,$|\overrightarrow Q| = 12$,and $|\overrightarrow R| = 13$.Since $\overrightarrow P + \overrightarrow Q = \overrightarrow R$,these vectors form a right-angled triangle because $5^2 + 12^2 = 25 + 144 = 169 = 13^2$.In the triangle formed by these vectors,$\overrightarrow Q$ and $\overrightarrow R$ meet at an angle $	heta$.Using trigonometry in the right-angled triangle,the cosine of the angle $	heta$ between $\overrightarrow Q$ and $\overrightarrow R$ is given by the ratio of the adjacent side to the hypotenuse.$\cos 	heta = \frac{|\overrightarrow Q|}{|\overrightarrow R|} = \frac{12}{13}$.Therefore,$	heta = \cos^{-1}(\frac{12}{13})$.

If vectors $\overrightarrow P, \overrightarrow Q$ and $\overrightarrow R$ have magnitudes $5, 12$ and $13$ units respectively and $\overrightarrow P + \overrightarrow Q = \overrightarrow R$,then the angle between $\overrightarrow Q$ and $\overrightarrow R$ is

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