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Question

In a ΔPQR, let a=QR,b=RP andc=PQ. If |a|=12,|b|=43 and b.c=24, then which of the following is/are true:

A
c22a=12
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B
c22+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
Using vectors summation method, a=b+c
Squaring both sides, we have:
|a|2=|c|2+|b|2+2cb
|c|2=122(43)22×24
c=43
|c|22|a|=12
Now, we also have:
c=a+b
Squaring both sides, we have:
|c|2=122+(43)2+2ab
144+48+2a.b=48a.b=72
a+b+c=0a×b+a×c=a×0
a×b+c×a=2a×b
=2|a|2|b|2(a.b)2=2(144)(48)(72)2=483

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