3D geometry problem- 5th Feb

Question

Line joining the points !!(2,-3,1)!! and !!(3,-4,-5)!! intersect the coordinate axes planes at ?

!!a)" "(0,-1,13)!!

!!b)" "(9,-9,0)!!

!!c)" "(-1,0,19)!!

!!d)" "(0,-1,6)!!

Solution

Equation of line:

!!(x-2)/-1 = (y+3)/1 = (z-1)/6 = lambda!!

Now, at !!yz!! Plane, !!x=0!!

!!(0-2)/-1 = lambda!!

!!=> lambda = 2!!

Hence, !!y = -3 + 2 = -1!!

and !!z = 1 + 12 = 13!!

Hence, Point (0,-1,13)

Again at !!xz!! Plane, !!y=0!!

!!(0+3)/1 = lambda!!

!!=> lambda = 3!!

Hence, !!x = 2 - 3 = -1!!

and !!z = 1 + (6*3) = 19!!

Hence, Point (-1,0,19)

Again at !!xy!! Plane, !!z=0!!

!!(z-1)/6 = (0-1)/6 = lambda!!

!!=> lambda = -1/6!!

Hence, !!x = 2 + 1/6 = 13/6!!

and !!y = -3 - 1/6 = -19/6!!

Hence, Point (13/6,-19/6,0)