Let A =2 i + k , ~B = i + j + k and C =4 i -3 j +7 k . If a vector R satisfies R B = C B and R A =0 , then R is given by

Step-by-step solution

aligned & R B = C B & A ( R B )= A ( C B ) & ( A B ) R -( A R ) B =( A B ) C -( A C ) B & ( A B ) R -0=( A B ) C -( A C ) B aligned aligned & R = C - ( A C ~A ~B ) B & ~A C =(2 i + k ) (4 i -3 j +7 k ) & =2(4)+0(-3)+1(7) & =15 & ~A ~B =(2 i + k ) ( i + j + k ) & =2(1)+0(1)+1(1) & =3 & R =4 i -3 j +7 k - ( 15 3 )( i + j + k ) & =4 i -3 j +7 k -5( i + j + k ) & =- i -8 j +2 k aligned