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Question

Let ΔPQR be a triangle. Let a = QR, b = RP and c = PQ. If |a|=12, |b|=43 and b.c=24, then which of the following is/are true ?


A

|c|22|a|=12

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B

|c|22+|a|=30

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C

|a×b+c×a|=483

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D

a.b=72

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Solution

The correct option is D

a.b=72



Given, |a|=12, |b|=43|a|=12, |b|=43a+b+c=0 a=(b+c)
We have, |a|2=|b+c|2
|a|2=|b|2+|c|2+2b.c 144=48+|c|2+48 |c|2=48|c|=43Also, |c|2=|a|2+|b|2+2a.b 48=144+48+2 a.b a.b=72
Option (d) is correct.
Also, a×b=c×a
a×b+c×a=2a×b|a×b+c×a|=2a×b|a×b+c×a|=2|a×b|=2|a|2|b|2(a.b)2=2(144)(48)(72)2=2(12)4836=483
Option (c) is correct.
Also,|c|22|a|=2412=12
Option (a) is correct.
and |c|22+|a|=24+12=36
Option (b) is not correct.


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