Find the vector that satisfies the following conditions.

Parallel to the plane 2x + 4y − 3z = 1 and through the

point (1, 0, −1)

I understand the method of doing vectors with 3 points, so I was thinking of extracting 2 more points from the equation, finding the perpendicular plane, and then change the equation so that it becomes parallel.

Frankly, i think my methodology is loony. It's the best I got right now, though.

Thanks!