The maximum and minimum magnitudes of the resultant of two vectors are 23 units and 7 units respectively. If these two vectors are acting at right angles to each other, the magnitude of their resultant will be
A
14
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B
15
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C
16
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D
17
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Solution
The correct option is D17 Let us assume two vectors are P and Q,
Maximum magnitude of resultant vector is, P+Q=23 -------------- (1)
And, Minimum magnitude of resultant vector is, P−Q=7 ----------------(2)
Adding equations (1) and (2), we get ⇒p=15
Hence from equation (1), Q=23−15=8
If →P⊥→Q,
Then magnitude of their resultant is, R=√P2+Q2=√225+64 R=17