Determine the point of intersection. L1: (x+10)/1=(y-4)/1=(z-8)/4 L2: (x+8)/2=(y+5)/3=(z+18)/7

Answer 1

Note that each double equals signs represents 3 equations:

x+10=y-4=(z-8)/4 => x+10=y-4, 4(x+10)=z-8, and 4(y-4)=z-8, and

(x+8)/2=(y+5)/3=(z+18)/7 => 3(x+8)=2(y+5), 7(x+8)=2(z+18), and 7(y+5)=3(z+18).

Start with the corresponding x,y pair of equations, to find the common (x,y) solution.

x+10=y-4 and 3(x+8)=2(y+5) => x=14, y=28

Then find z using any of the equations including z

4(x+10)=z-8, x=14 => z=104.

However, we have only shown that both lines go through a point of the form (14,28,z), and that for L1 (I used an L1 z-equation), z=104, but for L2, z=59.

The lines do not intersect. (They are skew.)