Find the vector equation of the line which is parallel to the vector and which passes through the point (1,–2,3).

We are given with,

Vector =

Point = (1, -2, 3)

This point can be written in the form of vector as .

Let,

We need to find the vector equation of the line which is parallel to the vector and passes through the point .

We know that,

Vector equation of a line passing through a point and parallel to a given vector is given as,

Where, λ ∈ ℝ

To re-phrase, we need to find .

Just substitute values of the vectors and in the above equation. We get,

This can be further rearranged or just be represented as it is.

On rearranging,

Thus, the required vector equation of the line is or can be written as .