3D line from two points and how too split the line?

[g242]

Hi!
I have a set of data points in excel with start_point (x1,y1,z1) and end_point (x2,y2,z2). Now i want to split the line into diffrent zones and further use the lenght in each zone for my calculation.

Lets say i have a line with coordinates (2,5,4) and (0,2,-6), dont want the line above z=0 (not cross the xy-plane). How can i split the line there, and calculate the length from this new point? (x',y',0)? I guess i have to use 3D pythagoras, but im kinda lost. I want to make this calculation automatic in excel.

 

[Deleted member 4993]

Hi!
I have a set of data points in excel with start_point (x1,y1,z1) and end_point (x2,y2,z2). Now i want to split the line into diffrent zones and further use the lenght in each zone for my calculation.

Lets say i have a line with coordinates (2,5,4) and (0,2,-6), dont want the line above z=0 (not cross the xy-plane). How can i split the line there, and calculate the length from this new point? (x',y',0)? I guess i have to use 3D pythagoras, but im kinda lost. I want to make this calculation automatic in excel.

Do you know the form of the equation of a line in 3-D?

 

[HallsofIvy]

A line in three dimensions can be written in "parametric form". In particular, the equation of the line through \(\displaystyle (x_1, y_1, z_1)\) and \(\displaystyle (x_2, y_2, z_2)\) can be written as \(\displaystyle x= x_1+ (x_2- x_1)t\)
\(\displaystyle y= y_1+ (y_2- y_1)t\)
\(\displaystyle z= z_1+ (z_2- z_1)t\)

Calculate that using (2, 5, 4) and (0, 2, -6). To divide that into two "zones", above and below the xy-plane, determine t such that z= 0.