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.
Solution
The given plane is
Its normal vector is
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
Now equation of the plane, passing through origin (0, 0, 0) with normal vector
is
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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