Question

Find the vector equation of the plane determined by the points (1, 0, −1), (0, 1, 1) and (−1, 1, 0). Also nd the point of intersection of the line

Answer 1

Solution:

The equation of a plane passing through three points

$\begin{vmatrix} x-1 & y-0&z+1 \\ 0-1 & 1-0&1-(-1)\\ -1-1 & 1-0&1+0 \end{vmatrix}=0, \\ \begin{vmatrix} x-1 & y&z+1 \\ -1 & 1&2\\ -2 & 1&1 \end{vmatrix}=0, \\ x-1-z-1-4y+2z+2+y-2x+2=0,$

$-x-3y+z+2=0$ ,

$x+3y-z-2=0$ .

Answer:

$x+3y-z-2=0$ .