Two equal forces $\to F$ are acting such that the magnitude of their resultant is equal to F. They must be inclined at an angle of __ degrees

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Solution

Here $| \to A | = F; | \to B | = F a n d | \to R | = F; θ = ?$

Using the direct formula,

$R = \sqrt{A^{2} + B^{2} + 2 A B c o s θ} F = \sqrt{F^{2} + F^{2} + 2 F^{2} c o s θ} F = F \sqrt{2 (1 + c o s θ)} c o s θ = - \frac{1}{2} θ = 120^{\circ}$

In case you are wondering how that formula came –It’s the parallelogram law of vectors addition.

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Similar questions

Two equal forces $\to F$ are acting such that the magnitude of their resultant is equal to F. They must be inclined at an angle of __ degrees

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