The point of intersection of the line joining the points (-3, 4, -8) and (5, -6, 4) with the XY-plane is

Concept:

Equation of line passing through two points

• Let, points A(x₁, y₁, z₁ ) and B(x₂, y₂, z₂) lies on a line

Then equation of line: 

Calculation:

Given points: (-3, 4, -8) and (5, -6, 4)

Equation of line passing through points (-3, 4, -8) and (5, -6, 4)

Let,

So, x + 3 = 8λ ⇒ x = 8λ - 3

 y - 4 = -10λ ⇒ y = -10λ + 4

z + 8 = 12λ ⇒ z = 12λ - 8     ---(1)

Now given that the line intersects the XY plane so, z = 0,

From (1),

z =12λ - 8

⇒ 12λ - 8 = 0

⇒ λ = 8/12 = 2/3

∴x = 8λ - 3

⇒ x = 8(2/3) - 3

Also, y = -10λ + 4

So the point of intersection

Hence, option (1) is correct