Engineering
Mathematics
Vector Product of Two Vectors
Question

Let  a=i^    k^,  b=i^  +  j^  and  c=i^  +  2j^  +  3k^ be three given vectors. If r is a vector such that  r×b  =  c×b  and  r·  a  =  0, then the value of r·  b, is

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Solution

 a=i^k^,  b=i^+j^,  c=i^+2j^+3k^

 (rc)×b=0rc=λbr=c+λb

      ra=0

 a.c+λb.a=0

 λ=a.cb.a=4

 r.b=c.b+λ|b|2=9