Vector Parallel To Yz Plane

Sometimes it is convenient to use other vectors as base vectors.

Vector parallel to yz plane. Vector parallel to yz y z plane. In a natural extension the equation in describes the plane passing through point which is parallel to the yz plane. Describe three dimensional space mathematically. Hence 0 0 5b 0.

Let u 0 a b for some a and b. Apparently any vector of the form 0yz as long as y and z are equal should be parallel to the yz plane correct. If you go back and look at the coordinate plane points this is very similar to the coordinates for the y z y z plane except this time we have x 3 x 3 instead of x 0 x 0. Locate points in space using coordinates.

For u to be parallel with the yz plane u must be perpendicular to 1 0 0. Any two non parallel vectors could be used as base vectors to give any point in the plane of the two vectors. If a plane is parallel to the xy plane the z coordinates of the points in that plane do not vary. The yz y z plane has equation x 0 x 0 so all vectors that are parallel to the yz y z plane must be orthogonal to the normal vector of that plane x 0 x.

So in a 3 d coordinate system this is a plane that will be parallel to the y z y z plane and pass through the x x axis at x 3 x 3. That is every other vector in that plane could be expressed in terms of the base vectors just as we say 6i 4j to express a vector in the xy plane. As we have seen in the equation describes the vertical line passing through point this line is parallel to the y axis. No you are following you just think you arent.

Yes any 0bc will do it. Write the distance formula in three dimensions. Thus b 0.