Question Type 1: Finding vector equation of a line passing through two points Exercises

Write the vector equation of the line through $C(0,5,-2)$ and $D(-4,1,-6)$.

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

Rewrite the line $\vec{r}=(0,1,6)+k(4,2,1)$ in parametric form.

Verify whether the point $M(2,1,3)$ lies on the line given by $\frac{x-5}{2}=\frac{y-1}{3}=\frac{z}{1}\,.$

Determine the vector equation of the line through $A(2,-1,0)$ and $B(5,2,3)$.

Convert the line $\frac{x-3}{1}=\frac{y+2}{-2}=\frac{z-5}{4}$ into vector form.

Check if the point $(4,-2,5)$ lies on the line $\vec{r}=(1,0,2)+t(3,-1,1)\,.$

Find the vector equation of the line joining $E(3,0,1)$ to $F(-1,4,-2)$.

Determine if $N(7,4,1)$ lies on the line $\frac{x+1}{4}=\frac{y-2}{-1}=\frac{z-3}{2}\,.$

Express the line $\vec{r}=(2,-1,3)+s(-5,4,2)$ in symmetric form.

Verify whether $(0,3,4)$ lies on the line through $(2,1,2)$ in direction $( -2,2,3)$.

Rewrite the symmetric line $\frac{x}{2}=\frac{y-3}{3}=\frac{z+1}{-1}$ in parametric form.