Is it normal for coriander plants to grow this slender ? if not, what should I be doing to help the herb grow better ?
Normally when plants grow like this, it is because they are searching for the light. Your plant needs more sun. You could also add soil to the pot to help support the trunk. It looks like your pot is sunny, so maybe the edge of the pot shaded your plant when it first germinated.
Namita, don't worry. Just follow Odif's advice about sun and your coriander will thicken and grow. Most emerging plants look a bit leggy.
It looks like this little plantlet is "newly born", as it were. I absolutely agree that poor light is one of the factors at play here. I have this with my plantlets when I germinate seeds in the spring or fall. Warmth can also be an issue here. You can add some soil or you could use a support stick and tie the delicate stem to it until the plants matures a bit more. Can you give us an indication where you are living? That may play a roll as well. Good luck with your cilantro.