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Rama09 [41]
3 years ago
13

Find the point on the plane 4x+3y+z=10 that is nearest to​ (2,0,1). What are the values of​ x, y, and z for the​ point? x= 28 /

13 y = 3 / 26 z= 27 / 26 ​(Type integers or simplified​ fractions.)
Mathematics
1 answer:
MariettaO [177]3 years ago
4 0

Answer:

\frac{1}{\sqrt{26}}.

Step-by-step explanation:

The minimun distance between a point and a plane is the perpendicular distance. The formula is

d = \frac{|Ax_0+By_0+Cz_0+D|}{\sqrt{A^{2}+B^{2}+C^{2}}}

where (x_0,y_0,z_0)=(2,0,1), A=4, B=3, C=1 and D=-10. So, the distance is

d = \frac{|8+1-10|}{\sqrt{16+9+1}}

d =  \frac{|-1|}{\sqrt{26}}

d = \frac{1}{\sqrt{26}}.

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