Discussion Forum

If line joining parts A and B having position vectors  6a-4b+4c and -4c respectively and the line joining the points C and D  having position vectors -a-2b-3c and a+2b-5c intersect , then point of intersection is 

Answer:

Explanation:

Coordinate of points A and B  are (6,-4,4)  and (0,0,-4)  and coordinate of points C and D are (-1,-2,-3) and (1,2,-5)

Now , equation of line passing through (0,0,-4) and (6,-4,4) is

   $\frac{x-0}{6}=\frac{y-0}{-4}=\frac{z+4}{4+4}$=k   [say]

 $\Rightarrow$        x=6k, y=-4k

      and z=8k-4       ........(i)

 Again , equation of line passing through (-1,-2,-3) and (1,2,-5) is

  $\frac{x+1}{1+1}=\frac{y+2}{2+2}=\frac{z+3}{-5+3}$

 $\Rightarrow$       $\frac{x+1}{2}=\frac{y+2}{4}=\frac{3+3}{-2}$  ........(ii)

 Since, two lines are intersect , therefore point (6k,-4k,8k-4) satisfy Eq.(ii) , we get

   $\frac{6k+1}{2}=\frac{-4k+2}{4}= \frac{8k-4+3}{-2}$

 $\Rightarrow$     6k+1=-2k+1=-(8k-1)

$\therefore$    6k+1=-2k+1

$\Rightarrow$     8k=0

$\Rightarrow$   k=0

$\therefore$  x=6 x 0, y=-4 x0

 and z=8 x0-4

 $\Rightarrow$  x=0 , y=0 and z=-4

 Which is equal to the B coordinate