vain, vein, vane

Vain or vain means conceited, as in thinking highly of oneself or one's qualities--
"You're so vain, I'll bet you think this song is about you..."
He was annoyed when she dyed her hair, and thought it vain of her.
Vain or vain also means futile or pointless--
All of his efforts were in vain.
He made a vain attempt to stop the moving car.

Vein or vein ( rhymes with vain ) means a blood vessel in the body--
A vein is like a tiny tube through which blood flows.
He got so excited that a vein stood out on his forehead.
A vein of a leaf circulates water--
He put a piece of paper over the leaf and rubbed it with a crayon. You could see each vein clearly.
Vein or vein also means a line of ore running through a mine--
The miner yelled for joy when he struck a vein of gold.
There is a rich vein of copper in the new mine.
Vein may mean a line of thought or discussion-
To continue in the same vein, let's discuss the funding for the new roof.

Vane or vane ( rhymes with vain ) means a flat blade or shape fashioned to move with the wind or by some other means--
You can tell which way the wind is blowing by looking at the weather vane.
He made a weather vane shaped like a rooster for the roof of the barn.

Now that you know that, you can say--
"They followed the weather vane, as the map directed, and dug for months to find a vein of gold, but all in vain."

Note--"vanity" is the noun ( thing or idea ) form of "vain"--
"Vanity of vanities, all is vanity..."
She often chided him for his vanity.
Note # 2--a "vanity" or "vanity table" is a piece of furniture with a large mirror--
She sat combing her hair in front of the vanity.