For any vector r i ( r i )+ j ( r j )+ k ( r k ) is equal to

Step-by-step solution

Now, i ( r i ) aligned & =( i i ) r -( i r ) i & = r -r₁ i aligned aligned & Similarly, j ( r j )= r -r₂ j & and k ( r k )= r -r₃ k & ( i ( r i ))+( j ( r j ))+( k ( r k )) & =3 r - (r₁ i +r₂ j +r₃ k ) & =3 r - r =2 r aligned