Determine the co-ordinates of the point where the line through the points A (2, 3, 2) and B (5, 1, 6) crosses the XY- plane?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 3)

Answer 1

Given:

A(2, 3, 2) and B(5, 1, 6) are two points.

Concept:

The cartesian equation of a line passing through A(x₁, y₁, z₁) and B(x₂, y₂, z₂) is given by,

Calculation:

Here, x₁ = 2, y₁ = 3, z₁ = 2, x₂ = 5, y₂ = 1 and z₂ = 6

The cartesian equation of a required line is:

⇒

⇒ ---- equation (1)

The line crosses xy - plane , i.e., z = 0

So, by substituting z = 0 in equation (1), we get

⇒

⇒ and

⇒ 2x - 4 = - 3 and 2y - 6 = 2

⇒ 2x = 1 and 2y = 8

⇒ x = and y = 4

∴ The line AB crosses the XY-plane at (1/2, 4. 0)