The direction in which force (F=13 N) is applied is at (A) 90^∘ with the direction of motion of

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The direction in which force (F=13 N) is applied is at (A)...

The direction in which force $(F=13 \mathrm{~N})$ is applied is at (A) $90^{\circ}$ with the direction of motion of the train. (B) $\cos ^{-1} \frac{5}{13}$ with the direction of motion of the train. (C) $\cos ^{-1} \frac{5}{12}$ with the direction of motion of the train. (D) $\cos ^{-1} \frac{12}{13}$ with the direction of motion of the train.

The direction in which force $(F=13 \mathrm{~N})$ is applied is at
(A) $90^{\circ}$ with the direction of motion of the train.
(B) $\cos ^{-1} \frac{5}{13}$ with the direction of motion of the train.
(C) $\cos ^{-1} \frac{5}{12}$ with the direction of motion of the train.
(D) $\cos ^{-1} \frac{12}{13}$ with the direction of motion of the train.

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Key Concepts

Vector Decomposition

Vector decomposition is the process of breaking a force or other vector into its component parts along specified directions. This is especially useful in physics where a force can be split into parts that act in parallel and perpendicular to the direction of motion, allowing for simpler analysis of its effects.

Trigonometric Functions

Trigonometric functions, particularly the cosine function and its inverse (arccos), are employed to determine angles based on the ratios of the sides of a right triangle. They are essential in problems where the components of a force and their relationship to the overall magnitude and direction of the force are being analyzed.

Dot Product

The dot product is a mathematical operation on two vectors that results in a scalar. It involves multiplying the magnitudes of the vectors by the cosine of the angle between them. This product is used to determine the component of one vector in the direction of another and is key in analyzing forces applied at specific angles relative to a given direction.

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