How do I calculate the distance between the two parallel planes $x - 2 y + 2 z = 7$ $x - 2y + 2z = 7$ and $2 y - x - 2 z = 2$ $2y - x - 2z = 2$ ?

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How do I calculate the distance between the two parallel planes $x - 2 y + 2 z = 7$ $x - 2y + 2z = 7$ and $2 y - x - 2 z = 2$ $2y - x - 2z = 2$ ?

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Answer 1 · 2016-01-04T23:50:15

Choose a point in any of the planes and calculate the distance between this point and the other plane.
In case $d = 3$ $d=3$

Explanation:

If the planes are parallel, any point of one plane is at the same distance to the other plane.

Choosing a point in plane 1, with $y = 0$ $y=0$ and $z = 0$ $z=0$ :
$x - 2 \cdot 0 + 2 \cdot 0 = 7$ $x-2*0+2*0=7$ => $x = 7$ $x=7$ => $P (7, 0, 0)$ $P(7,0,0)$

Rearranging equation of second plane:
$- x + 2 \cdot y - 2 \cdot z - 2 = 0$ $-x+2*y-2*z-2=0$

Formula of distance between a point and a plane:
$d = \frac{| a \cdot x_{p} + b \cdot y_{p} + c \cdot z_{p} + d |}{\sqrt{a^{2} + b^{2} + c^{2}}}$ $d=(|a*x_p+b*y_p+c*z_p+d|)/sqrt(a^2+b^2+c^2$
$d = \frac{| (- 1) 7 + 2 \cdot (0) + (- 2) \cdot 0 - 2 |}{\sqrt{{(- 1)}^{2} + {(2)}^{2} + {(- 2)}^{2}}} = \frac{| - 7 + 0 + 0 - 2 |}{\sqrt{1 + 4 + 4}} = \frac{9}{3}$ $d=(|(-1)7+2*(0)+(-2)*0-2|)/sqrt((-1)^2+(2)^2+(-2)^2)=(|-7+0+0-2|)/sqrt(1+4+4)=9/3$ => $d = 3$ $d=3$

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How do I calculate the distance between the two parallel planes $x - 2 y + 2 z = 7$ $x - 2y + 2z = 7$ and $2 y - x - 2 z = 2$ $2y - x - 2z = 2$ ?

1 Answer

Explanation:

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How do I calculate the distance between the two parallel planes x−2y+2z=7x - 2y + 2z = 7 and 2y−x−2z=22y - x - 2z = 2?

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How do I calculate the distance between the two parallel planes $x - 2 y + 2 z = 7$ $x - 2y + 2z = 7$ and $2 y - x - 2 z = 2$ $2y - x - 2z = 2$ ?