Find equation of the plane that passes through a given point and is perpen. to

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In summary, we need to find a vector in the direction of the given line and use it to find the equation of the plane passing through the point (2,3,-5) and perpendicular to the line x = -1 - t, y = 4 + 3t, z = 4t. This can be done by finding the normal vector of the line and using it in the plane equation formula.
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Kawrider0133
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Find equation of the plane that passes through a given point and is perpen. to...

Point: (2,3,-5)
Perpendicular to the line: x = -1 - t, y = 4 + 3t, z = 4t

I've looked up many examples to similar problems but i just can't get the right answer to this one. Please Help!
 
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Kawrider0133 said:
Point: (2,3,-5)
Perpendicular to the line: x = -1 - t, y = 4 + 3t, z = 4t

I've looked up many examples to similar problems but i just can't get the right answer to this one. Please Help!
The direction of the line is perpendicular to the plane, so the direction of the line is parallel to the plane's normal.

Do you know how to find a vector in the direction of a given line?
Do you know how to find the equation of a plane given a point on the plane and the normal?
 

FAQ: Find equation of the plane that passes through a given point and is perpen. to

1. What is the equation of a plane that passes through a given point and is perpendicular to a given line?

The equation of a plane that passes through a given point (x1, y1, z1) and is perpendicular to a given line with direction vector (a, b, c) can be written as: ax + by + cz = d, where d = ax1 + by1 + cz1.

2. How do you find the equation of a plane given its normal vector and a point?

To find the equation of a plane given its normal vector (a, b, c) and a point (x1, y1, z1), you can use the formula: a(x-x1) + b(y-y1) + c(z-z1) = 0.

3. Can you find the equation of a plane if only two points are given?

No, the equation of a plane requires at least three points to be determined. If only two points are given, there are infinite planes that can pass through them.

4. How does the distance between a point and a plane affect the equation of the plane?

The distance between a point and a plane affects the value of d in the equation of the plane (ax + by + cz = d). The farther away the point is from the plane, the larger the value of d will be.

5. What is the normal vector of a plane and how is it related to the equation of the plane?

The normal vector of a plane is a vector that is perpendicular to the plane. It is represented by (a, b, c) in the equation of the plane (ax + by + cz = d). The coefficients a, b, and c represent the direction of the normal vector and can be used to find the angle between the plane and another line or plane.

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