Find the coordina

Let A (x₁, y₁, z₁) and B (x₂, y₂, z₂) trisect the line segment joining the points P (4, 2, -6) and Q (10, -16, 6).

⇒ A divides the line segment PQ in the ratio 1 : 2.

Then,

Comparing this information with the details given in the question, we have

x₁ = 4, y₁ = 2, z₁ = -6; x₂ = 10, y₂ = -16, z₂ = 6 and m = 1, n = 2

By section formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) internally in the ratio m : n is given by:

So, we have

The coordinates of A =

Similarly, We know that B divides the line segment PQ in the ratio 2 : 1.

Then,

Comparing this information with the details given in the question, we have

x₁ = 4, y₁ = 2, z₁ = -6; x₂ = 10, y₂ = -16, z₂ = 6 and m = 2, n = 1

By section formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) internally in the ratio m : n is given by:

So, we have

The coordinates of B =

Hence, the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6) are (6, -4, -2) and (8, -10, 2).