Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the equations of the planes that passes through three points. (b) (1, 1, 0), (1, 2, 1), (– 2, 2, – 1)

6  Find the equations of the planes that passes through three points.

  (b)      (1, 1, 0), (1, 2, 1), (– 2, 2, – 1)

Answers (1)

best_answer

The equation of the plane which passes through the three points A(1,1,0),\ B(1,2,1),\ and\ C(-2,2,-1)  is given by;

Determinant method,

\begin{vmatrix} 1 &1 &0 \\ 1& 2 & 1\\ -2& 2 &-1 \end{vmatrix} = (-2-2)-(2+2)= -8 \neq 0

As determinant value is not equal to zero hence there must be a plane that passes through the points A, B, and C.

Finding the equation of the plane through the points, (x_{1},y_{1},z_{1}), (x_{2},y_{2},z_{2})\ and\ (x_{3},y_{3},z_{3})

\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

After substituting the values in the determinant we get,

\begin{vmatrix} x-1 &y-1 &z \\ 0& 1 &1 \\ -3& 1&-1 \end{vmatrix} = 0

\Rightarrow(x-1)(-1-1)-(y-1)(0+3)+z(0+3) = 0

\Rightarrow-2x+2-3y+3+3z = 0

2x+3y-3z = 5

So, this is the required Cartesian equation of the plane.

Posted by

Divya Prakash Singh

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question