Find parametric eq for a line with point and plane

In summary, to find the parametric equations for the line through Po=(3,-1,1) perpendicular to the plane 3x+5y-7z=29, we can use the normal to the plane as the direction vector for the line.
  • #1
marquitos
9
0
Find parametric equations for the line through Po=(3,-1,1) perpendicular to the plane 3x+5y-7z=29.


Hey guys I am slightly confused on where to even start on this one the only way i can think about doing it would be finding two other coordinates on the and then taking the cross product of the two vectors but honestly I am not really sure how to obtain the other two points either. So any help would be nice i might just be over thinking it. Thank you.
 
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  • #2
well i would go,

|x|...|3| ...|3|
|y|= |-1|+t|5|
|z|...|-1| ..|-7|

then you have x = 3+3t , y= -1+5t, and z = -1-7t

is this of any help?
 
Last edited:
  • #3
marquitos said:
Find parametric equations for the line through Po=(3,-1,1) perpendicular to the plane 3x+5y-7z=29.


Hey guys I am slightly confused on where to even start on this one the only way i can think about doing it would be finding two other coordinates on the and then taking the cross product of the two vectors but honestly I am not really sure how to obtain the other two points either. So any help would be nice i might just be over thinking it. Thank you.

Remember that the normal to the plane (which is obvous, no?) will do for a direction vector for the line.
 

FAQ: Find parametric eq for a line with point and plane

What is a parametric equation for a line with a given point and plane?

A parametric equation for a line with a given point and plane is a set of equations that represent the coordinates of points on the line in terms of one or more parameters. These equations can be used to determine the coordinates of any point on the line, making it easier to visualize and work with.

How do you find the parametric equation for a line with a given point and plane?

To find the parametric equation for a line with a given point and plane, you will first need to determine the direction vector of the line. This can be done by finding the difference between any two points on the line. Then, use the point and direction vector to write the parametric equations in terms of the parameter t.

What is the importance of finding the parametric equation for a line with a given point and plane?

Finding the parametric equation for a line with a given point and plane can help in many ways. It can be used to determine the coordinates of any point on the line, to graph the line, to find the distance between the line and other objects, and to solve problems involving the line and plane.

What is the difference between vector form and parametric form of a line with a given point and plane?

The vector form of a line with a given point and plane represents the line using a vector equation, while the parametric form uses parametric equations. In vector form, the direction vector of the line is multiplied by a scalar parameter, while in parametric form, the coordinates of points on the line are written in terms of the parameter t.

Can the parametric equation for a line with a given point and plane have multiple forms?

Yes, the parametric equation for a line with a given point and plane can have multiple forms. This is because there can be different choices for the direction vector and parameter, resulting in different equations that represent the same line. However, all forms will still represent the same line and can be used interchangeably.

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