Question Type 1: Given two points, finding the vector equation of a line Exercises

Determine the vector equation of the line through points $P(1,0,2)$ and $Q(4,0,8)$.

Find the vector equation of the line passing through $P(0,-2,4)$ and $Q(4,-2,0)$.

Determine the vector equation of the line passing through $P(5,0,0)$ and $Q(5,0,7)$.

Determine a vector equation of the line through $P(3,7,1)$ and $Q(-2,7,1)$.

Find the vector equation of the line passing through $P(1, 2)$ and $Q(4, 5)$ in the plane.

Find the vector equation of the line through $P(-1, -1, -1)$ and $Q(2, 3, 4)$.

Find the vector equation of the line passing through $P(1, 4, 3)$ and $Q(-1, 2, 1)$.

Determine the vector equation of the line through points $(-2, 4, 0)$ and $(3, -1, 2)$.

Given $P(a,2,3)$ and $Q(5,b,7)$, express the vector equation of the line passing through $P$ and $Q$ in terms of $a$ and $b$.

Find the vector equation of the line passing through $P(2,-3,5)$ and $Q(2,5,-1)$.

Determine the vector equation of the line through $A(0,0,0)$ and $B(1,1,1)$.

Find the vector equation of the line through $P(0,3,-2)$ and $Q(3,3,3)$.