Question Type 1: Using three points to write vector equation of a plane Exercises

Write the vector equation of the plane through $A(-2,0,5)$, $B(1,3,2)$ and $C(4,-1,3)$.

Find a vector equation of the plane containing $A(3,3,3)$, $B(6,2,1)$ and $C(1,5,4)$.

Determine a vector equation of the plane containing $A(-1,2,0)$, $B(0,3,4)$ and $C(2,1,1)$.

Find the vector equation of the plane through $A(0,1,-1)$, $B(-2,4,3)$ and $C(3,-1,2)$.

Find the vector equation of the plane through points $A(0,0,0)$, $B(2,1,3)$ and $C(1,4,2)$.

Find the vector equation of the plane containing $A(0.5,1.5,-2.5)$, $B(2.5,-0.5,3.5)$ and $C(-1.5,2.5,0.5)$.

Find the vector equation of the plane passing through $A\left(\frac{1}{2},0,1\right)$, $B\left(0,\frac{1}{2},-1\right)$ and $C\left(1,-\frac{1}{2},2\right)$.

Determine the vector equation of the plane through $A\left(\frac{2}{3},-\frac{1}{3},1\right)$, $B\left(\frac{5}{3},\frac{2}{3},-2\right)$ and $C\left(-1,\frac{4}{3},0\right)$.

Write the vector equation of the plane passing through points $A(1,2,3)$, $B(4,0,-2)$, and $C(-1,3,1)$.

Write the vector equation of the plane through $A(1,1,1)$, $B(1,2,3)$ and $C(2,0,1)$.

Find a parametric vector equation of the plane passing through the points $A(1,0,1)$, $B(3,1,-1)$, and $C(1,-1,2)$.

Using points $A(2,-1,0)$, $B(0,1,3)$ and $C(3,2,1)$, find the vector equation of the plane they determine.