Question

The ratio between maximum and minimum values of two vectors $\vec{A}$ and $\vec{B}$ ($\vec{A}>\vec{B}$) is 1:4. Then the ratio between the magnitudes of two vectors is

• A. 3:2
• B. 5:3
• C. 2:3
• D. 3:5

Hint:

Use the componendo-dividendo rule: if $(A+B)/(A-B) = 4/1$, then $A/B = (4+1)/(4-1) = 5/3$.

Answer 1

The Correct Option is D

Step 1: Concept
The maximum value of two vectors is $A+B$ and the minimum value is $A-B$.

Step 2: Meaning
The problem provides the ratio $(A-B) / (A+B) = 1/4$ (since $1:4$ implies the smaller value is first).

Step 3: Analysis
$4(A-B) = 1(A+B) \implies 4A - 4B = A + B \implies 3A = 5B$.

Step 4: Conclusion
The ratio $A/B = 5/3$. However, if we take the ratio $B/A$, it is 3:5.
Final Answer: (D)