Hi Kathy

I wouldn't recommend either a jig saw or a power plane for this job.

A power plane is made to shave a surface. I'd use it once you got a board down to around 1/8" of the finished width. But it won't make a straight cut, let alone a parallel one. It's actually the opposite of that. You often use a plane to get a board to fit against something that's not quite straight. If you use one, be sure the board is well secured. A power plane can be dangerous.

Many jig saws come with guides for making a straight cut but they have another problem. Because the thin blade is only supported on one end it tends to wander though the wood. It's usually impossible to get a perfectly perpendicular cut with a jig saw, especially in 1-by hardwood.

You would normally use a table saw for this or, alternatively, a jointer.