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  • Find the equation of plane passing through the points A (3, 2, 1), B (4, 2, 22) and C (6, 5, 21) and hence find the value of  for which A (3, 2, 1),B (4, 2, 22), C

Find the equation of plane passing through the points A (3, 2, 1), B (4, 2, 22) and C (6, 5, 21) and hence find the value of \lambda for which A (3, 2, 1),B (4, 2, 22), C (6, 5, 21) and D (\lambda, 5, 5) are coplanar.

 

 

 

 
 
 
 
 

Answers (1)

Equation of the plane passing through the points A(3,2,1), B(4,2,-2) and C(6,5,-1) is:

\begin{vmatrix}x-3 & y -2 & z - 1 \\ 4-3 & 2-2 & -2-1\\6-3 & 5 -2 & -1-1 \end{vmatrix} = 0 \Rightarrow \begin{vmatrix}x-3 & y -2 & z - 1 \\ 1 & 0 & -3\\3 &3 & -2 \end{vmatrix} = 0

\Rightarrow 9 (x -3 ) - 7(y-2)+3(z -1) = 0

\Rightarrow 9x -7y + 3z - 16 =0\quad -(i) is the required plane. Now if A(3,2,1), B(4,2,-2), C(6,5,-1) and D(\lambda, 5, 5) are coplanar then F must satissfy (i) that is, 9\lambda -7\times 5+ 3\times 5 - 16 =0 \Rightarrow \lambda = 4

Posted by

Ravindra Pindel

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