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

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- Jul 26th 2011, 06:52 AMgrgrsanjayFind 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 - Jul 26th 2011, 07:04 AMSironRe: Find the correct Plane!!
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? - Jul 26th 2011, 11:43 AMSironRe: Find the correct Plane!!
Does this help you? Or? ...

- Jul 26th 2011, 11:58 AMPlatoRe: Find the correct Plane!!
- Jul 27th 2011, 05:09 AMgrgrsanjayRe: Find the correct Plane!!
- Jul 27th 2011, 05:30 AMSironRe: Find the correct Plane!!
This is the way I would do it:

Given a plane $\displaystyle \alpha$ and two points $\displaystyle P_1 (2,2,-1) ,P_2 (3,4,2) \in \alpha $ and the plane is parallel to a line who's direction ratios are $\displaystyle (7,0,6)$. In general the vector equation of a plane through one point $\displaystyle P_1$ and with two directions vectors $\displaystyle R,L$is: $\displaystyle P=P_1+kR+mL$. Now we already have (we work now in a three dimensional space):$\displaystyle (x,y,z)=(2,2,-1)+k(7,0,6)+mL$. Can you determine the other direction vector $\displaystyle L$?

. - Jul 27th 2011, 06:24 AMPlatoRe: Find the correct Plane!!
- Jul 28th 2011, 07:41 AMgrgrsanjayRe: Find the correct Plane!!
- Jul 28th 2011, 09:32 AMSironRe: Find the correct Plane!!
Ok :D, do you want to show me your solution?