91Ó°ÊÓ

Find the distance between the point and the plane. $$ \begin{array}{l} (3,2,1) \\ x-y+2 z=4 \end{array} $$

Write an equation whose graph consists of the set of points \(P(x, y, z)\) that are twice as far from \(A(0,-1,1)\) as from \(B(1,2,0)\)

In Exercises 89-92, verify that the two planes are parallel, and find the distance between the planes. $$ \begin{array}{l} x-3 y+4 z=10 \\ x-3 y+4 z=6 \end{array} $$

Verify that the two planes are parallel, and find the distance between the planes. $$ \begin{array}{l} 4 x-4 y+9 z=7 \\ 4 x-4 y+9 z=18 \end{array} $$

Verify that the two planes are parallel, and find the distance between the planes. $$ \begin{array}{l} -3 x+6 y+7 z=1 \\ 6 x-12 y-14 z=25 \end{array} $$

Verify that the two planes are parallel, and find the distance between the planes. $$ \begin{array}{l} 2 x-4 z=4 \\ 2 x-4 z=10 \end{array} $$

In Exercises \(93-96,\) find the distance between the point and the line given by the set of parametric equations. (1,5,-2)\(; \quad x=4 t-2, \quad y=3, \quad z=-t+1\)

Find the distance between the point and the line given by the set of parametric equations. (1,-2,4)\(; \quad x=2 t, \quad y=t-3, \quad z=2 t+2\)

Find the distance between the point and the line given by the set of parametric equations. (-2,1,3)\(; \quad x=1-t, \quad y=2+t, \quad z=-2 t\)

Find the distance between the point and the line given by the set of parametric equations. (4,-1,5)\(; \quad x=3, \quad y=1+3 t, \quad z=1+t\)