Question
Find the equation of the plane that passes through the point
and has the normal vector
.
Ask by Ball Todd. in Malaysia
Dec 26,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the plane is
.
Solution
To find the equation of the plane that passes through the point
and has the normal vector
, you can use the point-normal form of the equation of a plane.
The general form of the equation of a plane given a point
and a normal vector
is:
Plugging in the given values:
Now, expand and simplify the equation:
This can be rewritten as:
Final Equation of the Plane:
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Extra Insights
To find the equation of the plane that passes through the point
with a normal vector
, we can use the point-normal form of the equation of a plane, which is given by:
Here,
is the point the plane passes through, and
are the components of the normal vector. Plugging in our values, we get:
Expanding this equation:
Combining like terms:
Rearranging gives us the final equation of the plane: