Explore IDNLearn.com's extensive Q&A database and find the answers you need. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.
Sagot :
The equation for the plane through the points p(0, 1, 1), q(1, 0, 1) and r(1, 1, 0) is x + y + z = 2
Given,
Three points :- p(0, 1, 1), q(1, 0, 1), r(1, 1, 0)
We can take this as ([tex](x_{1} ,y _{1}, z_{1} ), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] respectively.
Thus,
The equation for the plane through the points
Here,
The formula of equation of the plane passing through three non collinear points
[tex]x-x_{1} y-y_{1} z-z_{1} \\x_{2} -x_{1} y_{2} -y_{1} z_{2} -z_{1} = 0\\x_{3} -x_{2} y_{3} -y_{2} z_{3} -z_{2}[/tex]
by substituting the values in the formula of equation of the plane
x-0 y-1 z-1
1-0 0-1 1-1 = 0
1-0 1-1 0-1
x y z
1 -1 0 = 0
1 0 -1
x(1) - (y-1)(-1) - (z-1)(-1) = 0
x + y - 1 + z - 1 = 0
x + y + z + 2 = 0
x + y + z = 2
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
Learn more about equation for the plane here: https://brainly.com/question/28175018
#SPJ4
The equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
For given question,
We have been given three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)
We need to find an equation for the plane through the given three points.
We know that the equation of the plane through the points [tex](x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)[/tex] is,
[tex]\begin{vmatrix}x-x_1 & y-y_1 & z-z_1\\x_2-x_1 & y_2-y_1 & z_2-z_1\\x_3-x_1 & y_3-y_1 & z_3-z_1\end{vmatrix}=0[/tex]
Assume that for given points,
[tex](x_1,y_1,z_1)=(0, 1, 1)\\\\(x_1,y_1,z_1)=(1, 0, 1)\\\\(x_1,y_1,z_1)=(1, 1, 0)[/tex]
So, the equation of the plane passing though given points would be,
[tex]\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1-0 & 0-1 & 1-1\\1-0 & 1-1 & 0-1\end{vmatrix}=0\\\\\\\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1 & -1 & 0\\1 & 0 & -1\end{vmatrix}=0\\\\\\\Rightarrow x(1-0)-(y-1)(-1-0)+(z-1)(1-0)=0\\\\\Rightarrow x+y-1+z-1=0\\\\\Rightarrow x+y+z=2[/tex]
Therefore, the equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2
Learn more about the equation of the plane here:
https://brainly.com/question/27190150
#SPJ4
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.
