Using the index notation, expand the following expressions or evaluate the expressions in $3-$

dimensional space.

a$)t_i={}_{ij}{n}_j$

b$){}_{\text{i}\text{j}\text{k}}{}_{\text{i}\text{j}\text{k}}$

c$)\frac{\text{d}\text{e}\text{l}{}_{ij}}{del{x}_j}+b_i=\frac{de{l}^2{u}_i}{del{t}^2}$

d$)p={}_{ii}$

e$)W=\frac{1}{2}{}_{ij}{}_{ij}$

f$){}_{ij}^{\text{'}}=Q_{ik}{Q}_{jl}{}_{kl}$