If a vector Ā is making an angle "∅" with positive y-axis then which of the following is correct.?
Correct answer: C. Ay= ACos∅
- A. Ax= ACos∅
- B. Ay= ASin∅
- C. Ay= ACos∅
- D. None
Explanation
When a vector of magnitude A makes an angle φ with the positive y-axis, its y-component is adjacent to the angle, so Ay = A cosφ. The x-component is opposite the angle, so Ax = A sinφ. Students often choose Ax = A cosφ by remembering the cosine rule without checking which axis forms the angle.
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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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