# Math Help - Plane....

1. ## Plane....

Write an equation for the plane that contains the point A = (4,5,-3) and that is perpendicular to the line through B = (5,-2,-2) and C = (7,1,4)

2. Originally Posted by stones44
Write an equation for the plane that contains the point A = (4,5,-3) and that is perpendicular to the line through B = (5,-2,-2) and C = (7,1,4)
Write the equation of the plane with normal $\overrightarrow {BC}$ and contains the point A.

3. Originally Posted by stones44
Write an equation for the plane that contains the point A = (4,5,-3) and that is perpendicular to the line through B = (5,-2,-2) and C = (7,1,4)
one way to write the equation of a plane is:

$ax + by + cz + d = 0$

here, $\bold{n} = \left< a,b,c \right>$ is the normal vector to the plane. here, your normal vector is the vector $\overrightarrow {BC}$, do you see why?

we begin with $a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$

where $(x_0,y_0,z_0)$ is a point the plane passes through. then we expand and simplify

4. Originally Posted by Jhevon
one way to write the equation of a plane is:

$ax + by + cz + d = 0$

here, $\bold{n} = \left< a,b,c \right>$ is the normal vector to the plane. here, your normal vector is the vector $\overrightarrow {BC}$, do you see why?

we begin with $a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$

where $(x_0,y_0,z_0)$ is a point the plane passes through. then we expand and simplify
2(x-5) + 3(y-4) + 2(z+3) = 0
2x-10+3y-12+2z-6 = 0
2x + 3y + 2z = 28

5. Originally Posted by stones44
2(x-5) + 3(y-4) + 2(z+3) = 0
2x-10+3y-12+2z-6 = 0
2x + 3y + 2z = 28
here you have n = <2,3,2>, that is incorrect

6. There is a minor mistake.
$\overrightarrow {BC} = \left\langle {2,3,6} \right\rangle$