Step 1: Recall what a unit cell is. A unit cell is the smallest repeating box of a crystal lattice. Its size and shape are described by three edge lengths $a$, $b$, $c$ and three angles between those edges. Step 2: Connect the three edges to the three axes. The three edges meeting at one corner of the cell point along the three crystallographic axes. By the usual convention the edge along the x axis is $a$, the edge along the y axis is $b$, and the edge along the z axis is $c$. Step 3: Read the labels in the figure. The diagram marks the three edges from a corner as $i$, $j$, $k$. These are simply the names given to the same three axis directions. Step 4: Match labels to standard edge lengths. Following the standard order, the first edge $i$ corresponds to $a$, the second $j$ to $b$, and the third $k$ to $c$. So $i=a$, $j=b$, $k=c$. Step 5: Eliminate the mismatched options. Options that swap $b$ and $c$ (giving $j=c$, $k=b$) or reverse the order ($i=c$, $k=a$) break the standard one to one assignment, so they are rejected. Step 6: State the answer. The only consistent assignment is option (1). \[ \boxed{i=a,\ \ j=b,\ \ k=c\ \ \text{(Option 1)}} \]
