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

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

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

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

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

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

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

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 points $(-2,4,0)$ and $(3,-1,2)$.

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

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$(0,-2,4)$ and Q$(4,-2,0)$.

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