# Two coplanar lines and finding the equation

In summary, the conversation discusses finding the equation for a coplanar line perpendicular to another line. The method used involves using the cross product to find one direction vector and choosing a point on the line as the position vector. The remaining point is then used to find the second direction vector. The concept of coplanarity and parallel lines is also mentioned.

## Homework Statement

Two coplanar lines, a and b are perpendicular to each other. a passes through the points (3,2,3) and (8,10,6). Find the equation for b if it passes through the point (7,49,25).

## Homework Equations

The equation were trying to find is r = [x,y,z] + s [x1,y1,z1] + t [x2,y2,z2]

## The Attempt at a Solution

Basically since the coordinates are perpendicular I used the cross product to find one direction vector. For my position vector I used (3,2,3). Now I'm not sure what to do with the last point (7,49,25) or what to do to find my second direction vector. I'm not even sure if I did the first part right. Help would be appreciated thanks!

EDIT: I originally posted this in a different section but somebody told me it'd be better if I post it here. So if a mod could remove the other thread in the physics section that'd be awesome.

welcome to pf!

have you drawn this?

you have three known points, B C and D, and you want the line through B perpendicular to CD

Thank you for the welcome :)

So I'm assuming B is (3,2,3) and C is (8,10,6) etc.
In that case how would I go about finding direction vectors if they're perpendicular? Is it a combination of cross product of B and C?

EDIT: Also the term coplanar, does that mean the vectors in the equation have to be a multiple?

come on!

it's a simple triangle question!

(you can use parallel lines, and cross products )

(coplanar means in the same plane … any vector in it will be a linear sum of any two distinct vectors in it)

I`m sorry I am really lost now. I subtracted (3,2,3) and (8,10,6) and got (5,8,3). So that is my position vector I hope.

So as it stands the equation is r= (5,8,3) + s (xyz) + t (xyz)

How do I get the other coordinates for vector s and t

I subtracted (3,2,3) and (8,10,6) and got (5,8,3).

yes, that's the direction of your line CD

so what is the line through B parallel to that?

tiny-tim said:

yes, that's the direction of your line CD

so what is the line through B parallel to that?

I thought that was the position vectorÉ And if its parallel does that mean that CD dot product by (7,49,25) will be zeroÉ

I thought that was the position vectorÉ And if its parallel does that mean that CD dot product by (7,49,25) will be zeroÉ

you've lost me

what is the line through B parallel to CD?

Im kinda lost too. And I got (0,-3,8)

EDIT: Realised bumping not allowed. Please delete post. Sorry!

## 1. How do you determine if two lines are coplanar?

To determine if two lines are coplanar, you can check if they lie in the same plane. This can be done by graphing the two lines and seeing if they intersect or if they are parallel. If they are parallel, they are coplanar. If they intersect, they are also coplanar.

## 2. What is the equation for finding the intersection point of two coplanar lines?

The equation for finding the intersection point of two coplanar lines is to set the two equations equal to each other and solve for the values of x and y. The resulting values will be the coordinates of the intersection point.

## 3. How do you find the equation of a line given two points on the line?

To find the equation of a line given two points, you can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, you can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Then, you can plug in the slope and one of the given points into the slope-intercept form to find the equation.

## 4. What is the importance of knowing the equation of two coplanar lines?

Knowing the equation of two coplanar lines can help you determine if they are parallel, intersecting, or coincident. It can also help you find the intersection point, which can be useful in solving many real-world problems involving lines and planes.

## 5. Can two lines with different slopes be coplanar?

Yes, two lines with different slopes can be coplanar. As long as they lie in the same plane, they are considered coplanar. This means that they can intersect at a point or be parallel to each other.

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