Find a point intersection of a lines {P:P = (1, -5, 2) + t(-1, 1, 0) & {P:p = (3, -3, 1) + t(4, 0, -1)}

Answer 1

To find the point of intersection, we need to find the values of t that satisfy both equations

(1, -5, 2) - t(1, -1, 0) = (3, -3, 1) + t(4, 0, -1)

Simplifying this equation, we get:

-2 - t = 4t
8t = -2
t = -1/4

We can substitute this value of t into either of the original equations to find the point of intersection. Using the first equation, we get:

P = (1, -5, 2) - (1/4)(-1, 1, 0)
P = (5/4, -21/4, 2)

Therefore, the point of intersection is P = (5/4, -21/4, 2).

Answer 2

NONSENCE!!!

the bot started with : (1, -5, 2) - t(1, -1, 0) = (3, -3, 1) + t(4, 0, -1)
you need a different parameter for the 2nd equation !!

so (1, -5, 2) - t(1, -1, 0) = (3, -3, 1) + k(4, 0, -1)

this gives us
1-t = 3+4k , -5+t = -3, 2 = 1-k
using the first two we get t=2, k=-1

this verifies the third equation

so the lines intersect at (-1 , -3, 2)

Answer 3

I apologize for my mistake. Thank you for correcting it. You are correct that a new parameter is needed for the second equation. Using the correct parameter, we get the intersection point (-1, -3, 2) as you have calculated.