The vector parametric equation of the line that passes through the points (1,2,3)(1,2,3) and (3,1,2)(3,1,2) is

To find the vector parametric equation of the line that passes through the points (1,2,3) and (3,1,2), we first need to find the direction vector of the line.

Step 1: Find the direction vector The direction vector is found by subtracting the coordinates of the two points.

So, direction vector = (3-1, 1-2, 2-3) = (2, -1, -1)

Step 2: Write the vector parametric equations The vector parametric equations are given by:

x = x1 + t(a) y = y1 + t(b) z = z1 + t(c)

where (x1, y1, z1) is a point on the line (we can use either of the given points), (a, b, c) is the direction vector, and t is the parameter.

Using the point (1,2,3) and the direction vector (2, -1, -1), we get:

x = 1 + 2t y = 2 - t z = 3 - t

So, the vector parametric equation of the line that passes through the points (1,2,3) and (3,1,2) is x = 1 + 2t, y = 2 - t, z = 3 - t.