Find the vector and the cartesian equations of the lines that passes through the origin and (5, –2, 3).

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 (0, 0, 0) and (5, -2, 3) are and , respectively.

So, The vector equation of the required line is:

⇒

Now, we 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 (0, 0, 0) and (5, – 2, 3) is