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

Options

A. B
B. C
C. D
D. A

Answer

A

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
`(x-0)/(6)=(y-0)/(-4)=(z+4)/(4+4)=k` [say]
`rArrx=k,=-4kandz=8k-4` . . .(i)
Again, equation of line passing through
(-1,-2,-3) and (1,2,-5) is
`(x+1)/(1+1)=(y+2)/(2+2)=(z+3)/(-5+3)`
`rArr" "(x+1)/(2)=(y+2)/(4)=(3+3)/(-2)` . . . (ii)
Since, two lines are intersect, therefore point
(6k,-4km8k-4) satisfy Eq. (ii), we get
`rArr" "6k+1=-2k+1=-(8k-1)`
`:." "6k+1=-2k+1`
`rArr" "8k=0rArrk=0`
`:." "x=6xx0,y=-4xx0andz=8xx0-4`
`rArrx=0,y=0andz=-4`, which is equal to the B coordinate.