1. ## Vector parallel

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!

2. Originally Posted by Truthbetold
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!
1. There doesn't exist only one vector parallel to the given plane but an unlimited number of parallel vectors.

2. To find one of them it is sufficient to calculate the coordinates of two points in the plane which determine a vector which is parallel to the plane.

3. As an example: $\displaystyle A \left(0, 0, -\frac13 \right)$ and $\displaystyle B\left(0, \frac14, 0\right)$ determine a vector $\displaystyle \vec v = \left(0, \frac14, \frac13 \right)$.
For further calculations use $\displaystyle \vec d = (0, 3, 4)$

4. From the wording of the question I assume that you are asked to determine the equation of a line passing through the given point and parallel to the plane. If so:

$\displaystyle \vec r = (1,0,-1)+t\cdot (0,3,4)$

But, as I#ve mentioned above, there are an unlimited number of such lines, which are situated in a plane parallel to the given plane.