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MATH / For a point P, let d₁, d₂ and d₃ represents the distances from P to the planes x−z=0, x−2y+z=0, and x+y+z=0. Let S be the set of points P such that d₁²+d₂²+d₃²=36.Find the region o…

Problem

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problem

For a point P,P, let d1,d_1, d2d_2 and d3d_3 represents the distances from PP to the planes x−z=0,x - z = 0, x−2y+z=0,x - 2y + z = 0, and x+y+z=0.x + y + z = 0. Let SS be the set of points PP such that d12+d22+d32=36.d_1^2 + d_2^2 + d_3^2 = 36.Find the region of the volume enclosed by S.S.
Plain-text mathematical notation (without MathML)
For a point P, let d₁, d₂ and d₃ represents the distances from P to the planes x−z=0, x−2y+z=0, and x+y+z=0.  Let S be the set of points P such that
d₁²+d₂²+d₃²=36.Find the region of the volume enclosed by S.
Original LaTeX notation
For a point $P,$ let $d_1,$ $d_2$ and $d_3$ represents the distances from $P$ to the planes $x - z = 0,$ $x - 2y + z = 0,$ and $x + y + z = 0.$  Let $S$ be the set of points $P$ such that
\[d_1^2 + d_2^2 + d_3^2 = 36.\]Find the region of the volume enclosed by $S.$

level

Level 4

type

Precalculus

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Source and history

task_id
6149c3ee-f2a0-5039-9148-8cc372d0debf
task_key
precalculus--test--6149c3ee-f2a0-5039-9148-8cc372d0debf
task_revision_id
1
config / split
precalculus / test

Official source

initial import