Two vectors of magnitude 3 & 4 have a resultant of 5. The angle between vectors is :
Correct answer: A. 90°
- A. 90°
- B. 45°
- C. 180°
- D. 270°
Explanation
The problem involves finding the angle between two vectors with magnitudes 3 and 4, resulting in a magnitude of 5 for their resultant vector. Applying the law of cosines to the vectors: |R|2 = |P|2 + |Q|2 + 2|P||Q|cos∅, we substitute in the given magnitudes: 52 = 32 + 42 + 2(3)(4)cos∅. Simplifying gives 25 = 9 + 16 + 24cos∅. Solving for cos∅, we find cos∅ = 0, which means ∅ = 90°. Thus, the vectors are perpendicular. Other options such as 45°, 180°, and 270° do not satisfy the geometric and trigonometric constraints of the problem.
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About Addition of Vectors
Vector addition combines directed quantities using the head-to-tail, parallelogram and component methods. Work includes finding the resultant magnitude and direction for two or more vectors, resolving vectors into perpendicular components, and distinguishing vector addition from scalar addition, where direction has no role.
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