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Published on: September 12, 2026

Three force of equal magnitude P acts on a particle. If their directions are parallel to sides BC, CA, AB of a triangle ABC. Show that magnitude of resultant is

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To find the resultant of three equal forces P acting at angles, we can use vector addition. The forces can be represented as vectors at 120° to each other based on the geometry of triangle ABC. Using the formula for the resultant of two vectors, \( R = \sqrt{P^2 + P^2 + 2P \cdot P \cdot cos(120°)} = \sqrt{P^2 + P^2 - P^2} = P \). The angle between any two forces is 120°. Therefore, the resultant of three equal forces is \( R = P \sqrt{3} \). Hence the magnitude of the resultant is \( R = P \sqrt{3} \). Thus, the required magnitude is displayed in the image.

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