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Question

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 D 17
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,
PQ=7 ----------------(2)
Adding equations (1) and (2), we get
p=15
Hence from equation (1), Q=2315=8
If PQ,
Then magnitude of their resultant is,
R=P2+Q2=225+64
R=17

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