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The maximum and minimum magnitudes of the resultant of two vectors are 17 units and 7 units respectively. Then the magnitude of the resultant when the vectors act perpendicular to each other is:

1. 14
2. 16
3. 18
4. 13

Correct answer: 13

Solution

For two vectors of magnitudes $a$ and $b$, the maximum resultant is $a+b=17$ and the minimum is $|a-b|=7$. Solving gives $a=12$ and $b=5$. When perpendicular, the resultant is $\sqrt{a^2+b^2}=\sqrt{144+25}=13$.

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