Question:
Among the given pair of vectors, the resultant of two vectors can never be 3 units. The vectors are
Among the given pair of vectors, the resultant of two vectors can never be 3 units. The vectors are
Updated On: Mar 30, 2025
- 1 unit and 2 units
- 2 units and 5 units
- 3 units and 6 units
- 4 units and 8 units
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The Correct Option is D
Solution and Explanation
The magnitude of the resultant \(R\) of two vectors \(A\) and \(B\) must satisfy the following inequality:
\[|A - B| \leq R \leq A + B\]
We need to check for which pair of vectors, the resultant cannot be 3 units.
- (A) 1 unit and 2 units \[|1 - 2| \leq R \leq 1 + 2\] \[1 \leq R \leq 3\] Here, \(R\) can be 3.
- (B) 2 units and 5 units \[|2 - 5| \leq R \leq 2 + 5\] \[3 \leq R \leq 7\] Here, \(R\) can be 3.
- (C) 3 units and 6 units \[|3 - 6| \leq R \leq 3 + 6\] \[3 \leq R \leq 9\] Here, \(R\) can be 3.
- (D) 4 units and 8 units \[|4 - 8| \leq R \leq 4 + 8\] \[4 \leq R \leq 12\] Here, the minimum value of \(R\) is 4. Therefore, \(R\) can never be 3.
Answer: The vectors are (D) 4 units and 8 units. The resultant can never be 3 units.
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