Question

write parametric equations of the line containing the point (2,3,5) and parallel to the line represented by x-2/-1

Answer 1

The parametric equations for the line passing through the point (2,3,5) and parallel to the direction vector <-1, 0, 0> are x = 2 - t, y = 3, and z = 5, where 't' is a parameter representing any real number.

Step-by-step explanation:

The question involves finding the parametric equations of a line that passes through a given point and is parallel to a given direction vector.

To answer this, we use the point provided, (2,3,5), as the point through which the line passes.

Since the direction vector is given as parallel to the vector represented by (x-2)/-1, we interpret this as the vector <-1, 0, 0>.

Parametric equations of the line can be written by setting parameters t as the coefficient of the direction vector and adding the point coordinates.

Therefore, the parametric equations of the line are:

• x = 2 - t
• y = 3
• z = 5

Here, 't' is a parameter that can take any real value, which allows us to find any point on the line by substituting a value for t.