Question:
The ratio between maximum and minimum values of two vectors \(\vec A\) and \(\vec B\), where \(A>B\), is \(4:1\). Then the ratio between the magnitudes of two vectors is
The ratio between maximum and minimum values of two vectors \(\vec A\) and \(\vec B\), where \(A>B\), is \(4:1\). Then the ratio between the magnitudes of two vectors is
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For two vectors, maximum resultant is \(A+B\) and minimum resultant is \(A-B\) when \(A>B\).
Updated On: May 7, 2026
- \(3:2\)
- \(5:3\)
- \(2:3\)
- \(3:5\)
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The Correct Option is B
Solution and Explanation
Concept:
For two vectors \(\vec A\) and \(\vec B\):
\[
\text{Maximum resultant}=A+B
\]
and
\[
\text{Minimum resultant}=A-B
\]
when \(A>B\).
Step 1: Given ratio is: \[ \frac{A+B}{A-B}=\frac{4}{1} \]
Step 2: Cross multiply. \[ A+B=4(A-B) \] \[ A+B=4A-4B \]
Step 3: Bring like terms together. \[ 4A-A=B+4B \] \[ 3A=5B \]
Step 4: Therefore: \[ \frac{A}{B}=\frac{5}{3} \] Hence, the ratio of magnitudes is: \[ \boxed{5:3} \]
Step 1: Given ratio is: \[ \frac{A+B}{A-B}=\frac{4}{1} \]
Step 2: Cross multiply. \[ A+B=4(A-B) \] \[ A+B=4A-4B \]
Step 3: Bring like terms together. \[ 4A-A=B+4B \] \[ 3A=5B \]
Step 4: Therefore: \[ \frac{A}{B}=\frac{5}{3} \] Hence, the ratio of magnitudes is: \[ \boxed{5:3} \]
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