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

step 1 Hello, welcome to this lesson in this lesson I've posed me the magnitude of the resultant force

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.
$$|\mathbf{a}|=30 \mathrm{Ib}, \quad\|\mathbf{b}\|=50 \mathrm{lb}, \quad \theta=150^{\circ}$$

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Key Concepts

Resultant Force

The resultant force is the single force obtained by vectorially adding two or more forces. It has both magnitude and direction, and its calculation often involves breaking forces into components or directly applying the law of cosines when the angle between them is known.

Vector Addition

This concept involves combining two or more vectors to form a single vector known as the resultant. In the context of forces, vector addition allows us to determine the net force acting on an object by considering the magnitude and the direction of each force.

Law of Cosines

The law of cosines is used to compute the magnitude of the resultant when two vectors make a known angle. It relates the lengths of the sides of a triangle to the cosine of one of its angles, which is crucial when determining the combined effect of two forces at an angle.

Angle Between Vectors

The angle between vectors influences the magnitude of the resultant when adding forces. It determines how much of each force contributes to the net effect, with larger angles (approaching 180 degrees) leading to greater cancellation between the vectors.

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