# Plane equations

1. Dec 7, 2008

### fazal

1. The problem statement, all variables and given/known data

a)Determine whether the following two planes 3x-y+z=2 and 2x+2y-4z=5 are parallel, orthogonal,coincident (same) or none.

b)Find the equation of the plane that contains the point (2,3,-1) and parallel to the plane 5x-3y+2z=10

c)Find the distance from the point (3,5,-8) to the plane 6x-3y+2z=28

2. Relevant equations

3. The attempt at a solution

2. Dec 7, 2008

### tiny-tim

Hi fazal!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

3. Dec 7, 2008

### fazal

for A)
take the dot product of the two normal vectors. if its zero then they're perpendicular ?
take the cross product of the two normal vectors. if its zero then they're parallel ?

For them to be the same they'd have to be linear multiples of eachother? how?

B)Parallel to the plane 5x-3y+2z=10 means a vector normal to the plane is (5, -3, 2). So the equation has the form 5x - 3y + 2z = d. To get d, substitute the point (2,3,-1).

therefore is the equation 5x-3y+2z=-1 after sub the above??
plse check for me....

c)For c, use the formula:

4. Dec 7, 2008

### fazal

plse assist to check

5. Dec 7, 2008

### HallsofIvy

Staff Emeritus
What are the normal vectors for these planes? Are they parallel? Are they perpendicular?

For two vectors to be parallel, not "the same", one has to be a multiple of the other: <3, 2, 1> and <6, 4, 2> are parallel because <6, 4, 2>= 2<3, 2, 1>.

Why would you need someone else to check for you? Is 5(2)- 3(3)+ 2(-1)= 1?

Is that supposed to be negative? A distance is never negative.