QUESTION

# Hi, I am posting a question from the topic 3-Dimensional Space in Calculus III. The prerequisite in solving this question is a) Understanding of equations of planes. b) Understanding of equation of

Hi,

I am posting a question from the topic 3-Dimensional Space in Calculus III. The prerequisite in solving this question is

a) Understanding of equations of planes.

b) Understanding of equation of normal vectors, vector cross product and perpendicular vector.

Question :

Determine an equation for the unique plane that passes through the points $$P(0,0,2)$$ ,$$Q(0,4,0)$$ , and $$R(8,0,0)$$

Equation of plane that passes through three points is given by

$$a(x-x_0)+b(y-y_0)+c(z-z_0)=0$$

where

$$x_0,y_0,z_0$$ is a point on the plane

$$\langle a,b,c\rangle$$  is a vector perpendicular to the plane.

We know that we should find cross product of two vectors to find a perpendicular vector. We find those two vector namely $$\vec{v1}$$ and $$\vec{v2}$$ using the given points.

Once we find the perpendicular vector of the plane , substitute the values of $$\langle a,b,c\rangle$$ into plane equation to get the required equation of plane. Please see the attached file for the answer with detailed explanation.