In which quadrant the two rectangular components of a vector have same sign ?
Correct answer: C. Both 1st and 3rd
- A. 1st
- B. 2nd
- C. Both 1st and 3rd
- D. 4th
Explanation
The x and y components have the same sign in the first quadrant, where both are positive, and in the third quadrant, where both are negative. Thus both the first and third quadrants satisfy the condition. Option a is a common mistake because it considers only positive components and forgets that two negative components also have the same sign.
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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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