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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a→=−i^−k^, b→=−i^+j^, c→=i^+2j^+3 k^
(r→−c→)×b→=0⇒r→−c→=λb→⇒r→=c→+λb→
∵ r→⋅a→=0
⇒a→.c→+λb→.a→=0
⇒λ=−a→.c→b→.a→=4
⇒r→.b→=c→.b→+λ|b→|2=9