At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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?
either can be initial
so firsst find your normal line
mmaybe if i show u visually it will be easy for u to do it yourself
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?
x = -2 is equivalent to -x = 2
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
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
\[u\times v\] gives the normal vector right
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).
pictures r nice :)
Yes, direction of normal vector is not affected by multiplying the vector by a nonzero scalar
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?
both are same, but `7x+y-11z-5=0` looks more neat
14x+2y-2z-10=0 also works
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.
it is an equation, multiplying the same thing both sides doesn't change it in mathematically
Or, whenever I get a negative constant for variable X, I'll just divide it by -1?
why do you care what point you start wid
you end up wid same answer either way right
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.
Just really really making sure
okay i got you, then just multiply -1 in the end to make it look neat :)