Police Scotland received a report that a car was on fire on Turnhigh Road, Whitburn, at around 3.20am on Friday, October 22.
The Scottish Fire and Rescue Service attended after the fire had spread to two other vehicles.
Nobody was injured but substantial damage was caused to all three cars.
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Officers are treating the fire as deliberate and are now appealing for anyone with information to get in touch.
Detective Constable Rachel Royan said: “Thankfully no-one was injured as a result of this reckless act.
“I am appealing to anyone who witnessed the incident or who has any information which may assist us to get in touch.
“I would also ask anyone in the area to check dashcam footage and private CCTV.”
Anyone with any information should contact 101 quoting incident 0319 of October 22, 2021.