Resultant Vector Calculator Using Parallelogram Law of Forces

Online resultant vector calculator using parallelogram law of forces which is used to calculate magnitude and direction of resultant vector with known magnitudes and angles.

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Online resultant vector calculator using parallelogram law of forces which is used to calculate magnitude and direction of resultant vector with known magnitudes and angles.

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Resultant Vector Calculation Formula:

Given below is the formula to calculate the magnitude and direction of the resultant vector. There are a two different ways to calculate the resultant vector, the head to tail method and parallelogram method. The head to tail method to calculate a resultant which involves lining up the head of the one vector with the tail of the other. The parallelogram method involves properties of parallelograms and boils down to a simple formula.

Formula Used:


Where, R = Magnitude of Resultant Vector α = Direction of Resultant Vector P = Magnitude of Vector P Q = Magnitude of Vector Q θ = Angle Between Two Vectors

Use our free online resultant vector calculator using parallelogram law of forces to calculate the magnitude and direction of the resultant vector for the given magnitude and angle of vectors. If the displacement vectors A, B, and C are added together, the result will be vector R(Resultant vector).

Resultant Vector: Vector refers to a graphical representation of the magnitude and direction of a physical entity like force, velocity, or acceleration. The resultant vector is the vector that results from adding two or more vectors together. In other words, it is the combination of two or more single vectors.

Example

Two vectors P and Q has a magnitude of 10N and 15N and the angle between the two vectors is 60 degrees.
Magnitude of Resultant Vector = √(10^2 + 15^2 + (2 x 10 x 15 x cos 60°))
= √(100 + 225 + (300 x 0.5))
= √(325 + (150))
= √(475)
= 21.79

Direction of Resultant Vector = tan-1 [(15 x sin 60°) / (10 + 15 x cos 60°)]
= tan-1 [(15 x 0.866) / (10 + 7.5)]
= tan-1 [12.99 / 17.5]
= tan-1 [0.7422]
= 36.6 degrees

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