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Q88 (CDS-I/2019) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

If two vectors A and B are at an angle e * 0 degree then

Result
Your answer: —  Â·  Correct: B
Explanation

The magnitude of the resultant of two vectors A and B is given by the formula |A + B| = √(|A|² + |B|² + 2|A||B| cos θ). When the angle θ between the vectors is 0°, the vectors are parallel and point in the same direction. In this specific case, cos 0° = 1, and the magnitude simplifies to |A + B| = √(|A|² + |B|² + 2|A||B|) = |A| + |B|. However, for any angle θ > 0°, the triangle inequality states that |A + B| < |A| + |B|. The question specifies θ = e * 0°, which is likely a typographical representation of θ ≠ 0° or a general case. In general vector addition, the sum of individual magnitudes |A| + |B| is always greater than or equal to the magnitude of the resultant |A + B|. Since the equality only holds at exactly 0°, for any non-zero angle, |A| + |B| > |A + B|.

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