Question Type 3: Finding the intersection of three planes Exercises

Determine the intersection point of the planes $x - 2y + z = 1$, $3x + y - z = 4$, and $2x - y + 2z = 5$.

Solve for the intersection of the planes $3x + 2y - z = 4$, $2x - y + 4z = 5$, and $x + 3y + z = 6$.

Solve for the common point of the planes:

Determine the intersection of the planes $5x - 2y + z = 3$, $x + y - 3z = -2$, and $2x - y + 4z = 7$.

Find the point where the planes $x + 2y + 3z = 13$, $2x - y + z = 3$, and $3x + y - 2z = -1$ intersect.

Solve for the unique intersection of the following system of equations: $\begin{aligned} x + y + z &= 1 \\ 2x + 3y + 4z &= 4 \\ 3x - 2y + z &= 2 \end{aligned}$

Find the intersection point of the planes $x + y + z = 6$, $2x - y + 3z = 14$, and $-x + 4y + z = 2$.

Find the intersection point of the planes $4x - y + 2z = 6$, $-x + 2y - 3z = -4$, and $3x + y + z = 8$.

Solve for the intersection of the planes $x - y + 2z = 0$, $2x + 3y - z = 9$, and $-3x + y + 4z = 5$.

Find the intersection of the planes $3x - 2y + z = 1$, $x + y - 4z = 2$, and $2x - 3y + 5z = 3$.

Find the common point of the planes $4x + y - z = 8$, $-2x + 3y + 2z = 1$, and $x + y + z = 6$.

Find the unique solution of the system given by $2x - y + 3z = 4$, $-x + 4y - z = -5$, and $3x + y + 2z = 7$.