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Let a =- i - k , b =- i + j and c = i +2 j +3 k 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

Correct answer

0

Step-by-step solution

aligned & r b = c b & ( r - c ) b =0 r - c + b & or r = c + b & aligned Given, r a =0 , taking dot product with a for Eq. (i). Now, r a = a c + a b = - a c a b [ r a =0] (i) From Eqs. (i) and (ii), we get r = c - a c a b b Taking dot with b , we get r b = c b - a c a b ( b b ) where, [ array l a =- i - k b =- i + j c = i +2 j +3 k array ] =(-1+2)- (-1-3) (1) (1+1)=1+8=9

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