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Q.

Let  a¯=i¯+2j¯+3k¯, b¯=i¯j¯+2k¯  and  c¯=5i¯3j¯+3k¯  be three vectors. If r¯  is a vector such that, r¯×b¯=c¯×b¯ and  r¯.a¯=0 , then 25r¯2  is equal to 

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a

336

b

339

c

560

d

449

answer is D.

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Detailed Solution

r¯×b¯=c¯×b¯r¯c¯b¯

r¯=c¯+tb¯1

Now, 1r.a¯=0t=a¯.c¯a¯.b¯=85

r¯=155c¯8b¯

5r¯=17,7,1

25r¯2=339

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