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

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

KEAMKEAM 2002

Solution:

$ P+Q=17 $ ...(1) $ P-Q=7 $ ...(2) $ \therefore $ $ P=12,Q=5 $ Hence, $ R=\sqrt{{{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta } $ $ =\sqrt{{{(12)}^{2}}+{{(5)}^{2}}+0} $ $ (\because \theta =90{}^\circ ) $ =13 units