To determine whether forces in pairs are pulling at right angles (90 degrees) to each other, we need specific information regarding the direction of each force. Typically, forces can be represented as vectors, where each vector has both a magnitude and a direction.
Here's a general approach to assess if two forces are acting at right angles to each other:
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Vector Representation: Represent each force as a vector with its direction noted (for example, using Cartesian coordinates).
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Dot Product: One way to determine if two vectors are perpendicular (at right angles) is to compute their dot product. If the dot product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is zero (\( \mathbf{A} \cdot \mathbf{B} = 0 \)), then the forces are at right angles.
- The dot product formula is: \[ \mathbf{A} \cdot \mathbf{B} = A_x B_x + A_y B_y \]
- If this value equals to zero, the two forces act at right angles.
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Angle Calculation: Alternatively, you can also use the angle between two vectors. If the angle \( \theta \) between the forces is \( 90^\circ \), they are perpendicular.
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Geometric Interpretation: If the forces are given graphically (e.g., on a Cartesian plane), you could also look at the angles and orientations of the arrows representing those forces.
To provide a specific assessment for your query, I would need the details of the three forces in each of the pairs you wish to analyze. Please provide the information regarding the direction of each force, and I'd be happy to help you determine the relationships between them!
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