Mathematics: Find the coordinates of the point (x,y,z)(x,y,z) on the plane z=2x+3y+3z=2x+3y+3 which is closest to the origin.

Find the coordinates of the point (x,y,z)(x,y,z)

Ответ:

smady

14.03.2022

The vector equation of the line through the origin perpendicular to the plane is
.. (x, y, z) = t(2, 3, -1)
so the point of interest will satisfy
.. 2(2t) +3(3t) -(-t) = -3
.. 14t = -3
.. t = -3/14
and its coordinates are (x, y, z) = (-3/7, -9/14, 3/14)

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Ответ:

mahagonylyric

22.09.2020

Mathematics

$\frac{2}{5}x-6=-2\\
2x-30=-10\\
2x=20\\
x=10$

$-3y+\frac{1}{4}=\frac{13}{4}\\
-12y+1=13\\
-12y=12\\
y=-1$

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Find the coordinates of the point (x,y,z)(x,y,z) on the plane z=2x+3y+3z=2x+3y+3 which is closest to the origin.

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