Three forces of magnitudes 6 N, 6 N, and √(72) N act at corner of cube along three sides as s

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Three forces of magnitudes 6 N, 6 N, and √(72) N act at...

Three forces of magnitudes $6 \mathrm{~N}, 6 \mathrm{~N}$, and $\sqrt{72} \mathrm{~N}$ act at corner of cube along three sides as shown in figure. Resultant of these forces is:(a) $12 \mathrm{~N}$ angle $\mathrm{OB}$ (b) $18 \mathrm{~N}$ along $\mathrm{OA}$ (c) $18 \mathrm{~N}$ along $\mathrm{OC}$ (d) $12 \mathrm{~N}$ along $\mathrm{OE}$

Three forces of magnitudes $6 \mathrm{~N}, 6 \mathrm{~N}$, and $\sqrt{72} \mathrm{~N}$ act at corner of cube along three sides as shown in figure. Resultant of these forces is:(a) $12 \mathrm{~N}$ angle $\mathrm{OB}$
(b) $18 \mathrm{~N}$ along $\mathrm{OA}$
(c) $18 \mathrm{~N}$ along $\mathrm{OC}$
(d) $12 \mathrm{~N}$ along $\mathrm{OE}$

Key Concepts

Vector Addition

Vector addition is the process of combining two or more vectors to produce a resultant vector. This involves adding the magnitudes and directions of individual force vectors so that the overall effect can be determined. In physics, this concept is crucial for understanding how multiple forces acting on a body combine to influence its motion.

Force Components

Force components refer to the breakdown of a force vector into parts along chosen coordinate directions, usually orthogonal. In many problems, especially in three-dimensional space, forces are resolved into components along the x, y, and z axes. This decomposition simplifies calculations such as finding the resultant force by allowing the separate algebraic addition of the components.

Resultant Force

The resultant force is the single force that has the same effect as all the individual forces acting together on a body. It is obtained by vector addition of the individual forces. Determining the magnitude and direction of the resultant force is important for predicting the acceleration and overall motion of the object according to Newton's laws.

Three-Dimensional Pythagorean Theorem

The three-dimensional Pythagorean theorem extends the familiar two-dimensional version to calculate the magnitude of a vector in three-dimensional space by taking the square root of the sum of the squares of its components along the three axes. This mathematical approach is key to finding the magnitude of the resultant force when the individual forces act perpendicularly.

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