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)