Question

Line passing through (2,-3,1) and (3,-4,-5) intersects ZX-plane at.......,Select the correct option from the given options.
(a) (-1,0,13)
(b) (-1,0,19)
(c) (13/6, 0, -19/6)
(d) (0,-1,13)

Answer 1

for solution refer attachment and option b is correct

Answer 2

Line passing through $(x_2,y_1,z_1)$ and $(x_2,y_2,z_2)$ is given as
$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

here, two points are (2, -3, 1) and (3, -4, -5)

hence, equation of line is ..
(x - 2)/(3 - 2) = (y + 3)/(-4 + 3) = (z - 1)/(-5 - 1)

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

line passing through ZX plane ,
equation of ZX plane is y = 0. put in equation of line .
so, (x - 2)/1 = (0 + 3)/-1 = (z - 1)/-6
(x - 2)/1 = -3 = (z - 1)/-6
(x - 2) = -3 => x = -1
(z - 1) = 18 => z = 19

hence, line intersects ZX plane at (-1, 0, 19)
hence, option (b) is correct.