If a vector α makes an angle θ with the x-axis its x-component is given as:
Correct answer: A. a cos θ
- A. a cos θ
- B. a sin θ
- C. a tan θ
- D. a sin α
Explanation
When a vector α makes an angle θ with the x-axis, its x-component can be calculated using the formula: x = a * cos(θ), where "a" represents the magnitude of the vector. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, the adjacent side represents the x-component of the vector, and the hypotenuse represents the magnitude of the vector. So, by multiplying the magnitude of the vector by the cosine of the angle θ, we can find the x-component of the vector. This formula is derived from the concept of trigonometry and is widely used in vector calculations.
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Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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