The vectors a and b represent two forces acting at the same point, and θis the smallest positive

step 1 As shown in the figure, we net A in the positive direction of the x -axis. And then we can decom

The vectors a and b represent two forces acting at the same...

The vectors a and b represent two forces acting at the same point, and $\theta$ is the smallest positive angle between a and b. Approximate the magnitude of the resultant force.
$$|\mathbf{a}|=5.5 \mathrm{Ib}, \quad\|\mathbf{b}\|=6.2 \mathrm{Ib}, \quad \theta=60^{\circ}$$

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Key Concepts

Vector Addition

Vector addition is the process of combining two or more vectors to produce a new vector called the resultant. In physics, this concept is essential for understanding how multiple forces interact when acting at a single point, as the magnitude and direction of the resultant force are determined by the combined effects of the individual vectors.

Law of Cosines

The law of cosines is used in vector addition when the vectors are not orthogonal to each other. It provides a method for calculating the magnitude of the resultant vector by relating the magnitudes of the individual vectors and the cosine of the angle between them, thereby generalizing the Pythagorean theorem for any angled scenario.

Resultant Force

The resultant force is the single force that has the same effect on an object as all the individual forces acting together. Its magnitude and direction are determined by vector addition, and it represents the net influence on the object's motion according to Newton's laws of motion.

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