Question

I find the points of intersection of the lines
and Ed Where A=(7,-6,1), B = (17,-18,-3)
C=(1,4,-5) and D=(3,-4, 11). Conta
AB​

Answer 1

Answer:

The given points are A (7, 6, 1), B (17, - 18, - 3), C (1, 4, - 5) and D (3, 4, 11)

The equations of the line AB are

(x - 7)/(17 - 7) = (y - 6)/(- 18 - 6) = (z - 1)/(- 3 - 1)

or, (x - 7)/10 = (y - 6)/(- 24) = (z - 1)/(- 4)

or, (x - 7)/5 = (y - 6)/(- 12) = (z - 1)/(- 2) = t (say)

Then x = 5t + 7, y = - 12t + 6, z = - 2t + 1 (1)

Again, the equations of the line CD are

(x - 1)/(3 - 1) = (y - 4)/(4 - 4) = (z + 5)/(11 + 5)

or, (x - 1)/2 = (y - 4)/0 = (z + 5)/16

or, (x - 1)/1 = (y - 4)/0 = (z + 5)/8 = u (say)

Then x = u + 1, y = 4, z = 8u - 5 (ii)

To find the point of intersection of the lines AB and CD, from (i) and (ii), we equate the corresponding values of x, y, z.

5t + 7 = u + 1 or, 5t - u + 6 = 0 (iii)

- 12t + 6 = 4 or, t = 1/6 (iv)

- 2t + 1 = 8u - 5 or, t + 4u - 3 = 0 (v)

Using (iv), from (iii), we get

5 (1/6) - u + 6 = 0

or, u = 5/6 + 6

or, u = 41/6

But the values t = 1/6 and u = 41/6 do not satisfy (v). So the lines do not intersect each other.

[ Refer to the image to see the lines not intersecting each other. ]

Similar type of problems:

1. Find the point of intersection of the lines joining the points (- 3, 7), (2, - 4) and (4, 6), (- 5, - 6). Also find the point of intersection of these lines and also their intersection with the axis. (graph)

2. Find the maximum points of intersection of 16 circles.

Step-by-step explanation: