Question #307586

Find the equation of the plane through the origin and parallel to the plane 10x+3y+7z=6


Blank 1. Calculate the answer by read surrounding text.


x+ Blank 2. Calculate the answer by read surrounding text.


y+ Blank 3. Calculate the answer by read surrounding text.


z= Blank 4. Calculate the answer by read surrounding text.




1
Expert's answer
2022-03-18T05:35:37-0400

Solution


The given plane is


10x+3y+7z=610x+3y+7z=6


Its normal vector is


n1=[10,3,7]\vec{n_{1}}=[10, 3, 7]


We know that if the two planes are parallel, then they have the same normal vector or their normal vectors are parallel (i.e they are integral multiple of each other)


Therefore, the normal vector of the required plane is


n2=[10,3,7]\vec{n_{2}}=[10, 3, 7]


Now equation of the plane, passing through origin (0, 0, 0) with normal vector

n2=[10,3,7]\vec{n_{2}}=[10, 3, 7] is


(x0)(10)+(y0)(3)+(z0)(7)=0(x-0)(10)+(y-0)(3)+(z-0)(7)=0


10x+3y+7z=010x+3y+7z=0


A plot of the required plane is shown below





Blank 1 --- 10


Blank 2 --- 3


Blank 3 --- 7


Blank 4 --- 0




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