Similar to how the distance formula can be modified to get 3 dimensions, can the same be done to the slope-formula?

Question

helder_edwin · Answer

the slope is the tangent of the angle between the line and the positive direction of the x-axis

helder_edwin · Answer

i guess that, in 3d, you could measure the angle between the line and the xy-plane and call its tangent the slope.

anonymous · Answer

Well, I'm asking this from the context that I have to find the area of a triangle using three dimensional coordinates...

helder_edwin · Answer

but if u r given two lines perpendicular to each other would the product of the slopes still be -1?

anonymous · Answer

Not quite sure...really...

helder_edwin · Answer

but if u have the 3 points that define the triangle u can measure the lengths of the sides and use (i'm not sure of the name) heron's formula

anonymous · Answer

Yeah. I know. It was just a spur of the moment question out of curiosity...

dumbcow · Answer

for 3-d, its better to think of slope as a directional vector with 3 components
the slope in 2-d is just a vector with 2 components: <1,m>

anonymous · Answer

I haven't done vectors, so for now, I'll just think that I shouldn't be using it yet. THanks! :)

dumbcow · Answer

oh nevermind then...then how are you supposed to determine slope in 3-d?

dumbcow · Answer

what level math are you in ?

anonymous · Answer

Algebra II, borderline pre-calc. Like I said, it was a spur of the moment question out of curiosity, so if I shouldn't know how to do it yet, I'll just save it for later.

dumbcow · Answer

haha yeah it will come later, vectors usually at end of pre-calc
so to answer your question, the formula for finding slope in 3-d is not quite as simple as the easy modification of distance formula

anonymous · Answer

Alright. Thank you :)