Isobel Zito

Plotting a three-dimensional point (a, b, c) in Cartesian System, we will locate a on the x-axis, move bunits parallel to the y-axis and lastly, we move c-units parallel to the z-axis.

In other words, the point (a, b, c) is the vertex diagonally opposing the origin in the box with lengths a, b, c and one vertex at the origin.

Knowing how to plot three-dimensional points in space helps us plotting a position vector in space.

The position vector with the components is the vector with the initial point at the origin and terminal point at (a, b, c).

Any vector in space has a unique position vector, but there are infinitely many vectors equal to a position vector, they are just translated to a different initial point than the origin.

Position vectors appear in the direction vector of a line or the normal vector to a plane or surface.

1. State the direction vector to the line x = -t, y = 1 - t, z = 3t, and plot the position vector of the direction vector.

2. State the normal vector to the plane -x + z = 5 and plot the position vector of the normal vector.

1. The position vector of the direction vector is <-1, -1, 3> shown by the red vector in the figure below