. Find the vector and the cartesian equations of the line that passes through the points (3, –2, –5), (3, –2, 6).

Question

Philoid · Accepted Answer

We know that

The vector equation of as line which passes through two points whose position vectors are and is .

Here, the position vectors of the two points (3, –2, –5) and (3, –2, 6) are and , respectively.

So, the vector equation of the required line is:

⇒

Now, we also know that

Cartesian equation of a line that passes through two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is

So, the Cartesian equation of the line that passes through the origin (3, -2, -5) and (3, -2, 6) is