Find the equation of the line passing through the point (2, –1, 3) and parallel to the line
Vector equation of a line is where is the position vector of the point a through which our line passes through and is the vector parallel to our line and is the general vector of a line satisfying these conditions and is a constant.
Now the point vector through which the line passes is = 2+3 and the required line is parallel to a line having vector equation,
= (–2+) + λ(2+3–5)
The parallel vector is,
= (2+3–5)
So the vector equation of the required line is,
= (2+3) + μ(2+3–5)
Where μ is a constant or a scalar.