Cosθi^ + Sinθj^ is a_________________?
Correct answer: D. The unit vector in the direction at angle θ with an x-axis
- A. Vector
- B. Position Vector
- C. Vector in the direction at angle θ with an x-axis
- D. The unit vector in the direction at angle θ with an x-axis
Explanation
The magnitude of cosθ i + sinθ j is sqrt(cos²θ + sin²θ) = sqrt1 = 1, so it is a unit vector. Its components give an angle θ with the positive x-axis because its x and y components are cosθ and sinθ. Option a is incomplete because it identifies only a vector, not the more specific unit-vector property.
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About Rectangular Components
A vector is resolved into perpendicular horizontal and vertical components using trigonometric relations, usually as Ax = A cos θ and Ay = A sin θ when θ is measured from the horizontal. Questions involve signs in different quadrants, reconstructing a resultant from components, and using components to analyse equilibrium.
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