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

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

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

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

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

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

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

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

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

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 passing through $A\bigl(\tfrac12,0,1\bigr)$, $B\bigl(0,\tfrac12,-1\bigr)$ and $C\bigl(1,-\tfrac12,2\bigr)$.

Determine the vector equation of the plane through $A\bigl(\tfrac23,-\tfrac13,1\bigr)$, $B\bigl(\tfrac53,\tfrac23,-2\bigr)$ and $C(-1,\tfrac43,0)$.

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