Vector Equation Of A Plane

Step 1: Find two vectors in the plane.
The vectors and are in the plane. They are given by:

Step 2: Find the normal vector to the plane.
The normal vector is given by the cross product of and : Using the formula for the cross product:

Step 3: Write the vector equation of the plane.
The vector equation of the plane is: Substituting and : Thus, the vector equation of the plane is:

Final Answer: The vector equation of the plane is:

Step 1: Recall the equation of a plane.
The vector equation of a plane passing through a point and perpendicular to a normal vector is given by:

Step 2: Identify the given quantities.
The position vector of the point is and the normal vector to the plane is .

Step 3: Write the equation of the plane.
The vector equation of the plane is:

Step 4: Compute the dot product on the right-hand side.

Step 5: Final equation of the plane.
Thus, the equation of the plane is:

Final Answer: