Zenmo
  • Zenmo
@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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Zenmo
  • 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
  • Zenmo
|dw:1435136878321:dw|
dan815
  • dan815
either can be initial

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dan815
  • dan815
so firsst find your normal line
dan815
  • dan815
mmaybe if i show u visually it will be easy for u to do it yourself
Zenmo
  • 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
  • dan815
|dw:1435144221416:dw|
ganeshie8
  • ganeshie8
x = -2 is equivalent to -x = 2
dan815
  • 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
  • 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
  • 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
  • ganeshie8
\[u\times v\] gives the normal vector right
dan815
  • dan815
yup
Zenmo
  • 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
  • dan815
pictures r nice :)
ganeshie8
  • ganeshie8
Yes, direction of normal vector is not affected by multiplying the vector by a nonzero scalar
Zenmo
  • 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
  • ganeshie8
both are same, but `7x+y-11z-5=0` looks more neat
ganeshie8
  • ganeshie8
14x+2y-2z-10=0 also works
Zenmo
  • 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
  • ganeshie8
it is an equation, multiplying the same thing both sides doesn't change it in mathematically
Zenmo
  • Zenmo
Or, whenever I get a negative constant for variable X, I'll just divide it by -1?
ganeshie8
  • ganeshie8
why do you care what point you start wid
ganeshie8
  • ganeshie8
you end up wid same answer either way right
Zenmo
  • 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
  • Zenmo
Just really really making sure
ganeshie8
  • ganeshie8
okay i got you, then just multiply -1 in the end to make it look neat :)

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