Q.Find the vector equation of the line passing through the points $A(1,0,2)$ and $B(3,4,-1)$.

A line through a point with position vector $\vec a$, parallel to a vector $\vec b$, has vector equation $\vec r=\vec a+\lambda\vec b$; equating components gives the Cartesian symmetric form $\dfrac{x-x_1}{a}=\dfrac{y-y_1}{b}=\dfrac{z-z_1}{c}$, where $a,b,c$ are the line's direction ratios. When two points are given instead of a point and …