Thread: Find the correct Plane.

Find the equation of the plane passing through the points (2,2,-1) and (3,4,2) and parallel to a line whose direction ratios are (7,0,6)

Thanks in Advance

A plane is determined by three points or by two direction vectors and a point, now you've given one direction vector and two points, so you need to find another direction vector.

EDIT:
Do you want a vector equation or a cartesian equation?

Does this help you? Or? ...

Originally Posted by grgrsanjay

Find the equation of the plane passing through the points (2,2,-1) and (3,4,2) and parallel to a line whose direction ratios are (7,0,6)

A plane is parallel to a line if the direction of the line is perpendicular to the normal of the plane.

Originally Posted by Siron

Does this help you? Or? ...

I need a Vector equation, I even need the steps please!

This is the way I would do it:
Given a plane and two points and the plane is parallel to a line who's direction ratios are . In general the vector equation of a plane through one point and with two directions vectors is: . Now we already have (we work now in a three dimensional space): . Can you determine the other direction vector ?
.

Originally Posted by grgrsanjay

I need a Vector equation, I even need the steps please!

Define vectors:

Note

Now the equation you want is

Originally Posted by Siron

This is the way I would do it:
Given a plane and two points and the plane is parallel to a line who's direction ratios are . In general the vector equation of a plane through one point and with two directions vectors is: . Now we already have (we work now in a three dimensional space): . Can you determine the other direction vector ?
.

I Couldn't Understand it completely....But the Good thing is that i understood fully what Plato Explained

So i think my problem is solved,
Thanks

Ok , do you want to show me your solution?