@Small Question, don't need to solve@
Find the general form of the equation of the plane with the given characteristics.
Passes through (2, 2, 1) and (-1, 1, -1) and is perpendicular to 2x-3y+z=3.

- Zenmo

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- Zenmo

For the points (2, 2, 1) and (-1, 1, -1). How do I know, which point is the initial point? Whichever z variable value is greater?

- Zenmo

|dw:1435136878321:dw|

- dan815

either can be initial

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- dan815

so firsst find your normal line

- dan815

mmaybe if i show u visually it will be easy for u to do it yourself

- Zenmo

So if the solution in the book is 7x+y-11z-5=0, but I put the answer as -7x-y+11z+5=0. I would still be correct?

- dan815

|dw:1435144221416:dw|

- ganeshie8

x = -2
is equivalent to
-x = 2

- dan815

you want to find your normal line of the plane, move that normal like to a point, then see the other line connecting p1 and p2, then u have 2 lines and u can define your plane now

- dan815

u can take the cross of these 2 lines to get your new normal
then the plane equation is
ax+by+cz=d
and u can find d but subbing in one of your points

- dan815

if that plane quations seems a little magical, u can get it more lgoically by computing the dot product of your normal line with one of your vectors in your plane,
dot =0 will also yield the same plane equation

- ganeshie8

\[u\times v\] gives the normal vector right

- dan815

yup

- Zenmo

ok, I got it now. Thanks for clarification. X = -2 is the same as -X = 2. Which, is the same as u x v = - ( v x u).

- dan815

pictures r nice :)

- ganeshie8

Yes, direction of normal vector is not affected by multiplying the vector by a nonzero scalar

- Zenmo

But, just to make sure. I can put the answer as -7x-y+11z+5=0, even though the solution is 7x+y-11z-5=0?

- ganeshie8

both are same, but `7x+y-11z-5=0` looks more neat

- ganeshie8

14x+2y-2z-10=0
also works

- Zenmo

so to get 7x+y-11z-5=0. I would have to start with the point (2, 2, 1) then. Which, comes back to the question of what initial point to use.

- ganeshie8

it is an equation, multiplying the same thing both sides doesn't change it in mathematically

- Zenmo

Or, whenever I get a negative constant for variable X, I'll just divide it by -1?

- ganeshie8

why do you care what point you start wid

- ganeshie8

you end up wid same answer either way right

- Zenmo

Yea, but the signs would be different, hence: -7x-y+11z+5=0 vs 7x+y-11z-5=0.
So, either format works, but the positive one looks neater.

- Zenmo

Just really really making sure

- ganeshie8

okay i got you, then just multiply -1 in the end to make it look neat :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.