your man needs help with vectors

[Mamba]

Hey guys stuck on a uni assignment. No matter how many times I've punched this into the formula I can't get the correct response.

Find the equation that passes through the points, (-2, -1, 4) (-1, 3, -4) and (11, 0, 1)

Any help would be perfect.

[nathanjizzle]

yikes

[cos88]

sekiy

[Budadiiii]

[oarabbus]

Hey guys stuck on a uni assignment. No matter how many times I've punched this into the formula I can't get the correct response.

Find the equation that passes through the points, (-2, -1, 4) (-1, 3, -4) and (11, 0, 1)

Any help would be perfect.

http://www.math.washington.edu/~king...equations.html


Check the section "Finding the equation of a plane through 3 points in space"

The equation of a plane is ax+by+cz=d
So for your problem, solve the system
-2x - 2y +4z = d
-x + 3y -4z = d
11x + z = d



solve for d in terms of a, b, and c
for example if you add the first two equations you'll have
-3x +y = 2d
Now substitute this back into the system until you've solved everything in terms of d


then substitute what you calculated into ax+by+cz = d, and choose a value for d to make the equation simple

EXAMPLE: if you solved your system to ultimately find a=d, b=2d, c=3d your equation will be
ax + by + cz =d ----> dx + 2dy + 3dz = d
(plug in d=1)
your final answer would be x + 2y + 3z = 1


let me know if that helps if not I'll see what I can do a little later


edit: another method to do the same thing

Given, P = (1, 1, 1), Q = (1, 2, 0), R = (-1, 2, 1). Find the equation of the plane through these points.

First, the normal vector is the cross product of two direction vectors on the plane (not both in the same direction!).

Let one vector be PQ = Q - P = (0, 1, -1) and the other be PR = R - P = (-2, 1, 0). The cross product

(Q - P) x (R - P) = (1, 2, 2) = normal vector A and the equation is A . X = d for some d

Using the method in the example above, we can find d = A . P = 5. Thus the equation is A . X = 5, which is the same as one of the equations in the earlier example.

[tmacattack33]

I ain't ever seen no damn 3-D graph problems like that.

Is it possible to just do two dimensions at a time or something?

Sh*t.

[highwhey]

Vectors and cross products are the point in physics class when the class size drastically reduced from 24 to about 10

[shaq2000]

Assuming Cartesian: