Question

The maximum and minimum magnitude of the resultant of two given vectors are 17 units and 7 unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

Moderate

Solution

$R_{\max} = A + B = 17 when θ = 0^{0}$
$R_{\min} = A - B = 7 when θ = 180^{0}$
By solving we get A = 12 and B = 5
Now when $θ = 90^{0} then R = \sqrt{A^{2} + B^{2}}$
$\Rightarrow R = \sqrt{{(12)}^{2} + {(5)}^{2}} = \sqrt{169} = 13$

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