Question

If z₁ and z₂ are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z₁ + z₂ = ______.

Options

• 1

• 4

• 5

• 10

Answer 1

If z₁ and z₂ are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z₁ + z₂ = 10.

Explanation:

C divides AB internally in the ratio 1 : 2 and
D divides AB internally in the ratio 2 : 1.

∴ `"z"_1 + "z"_2 = (1(6) + 2(4))/(1 + 2) + (2(6) + 1(4))/(2 + 1)`

`= 14/3 + 16/3`

`= 30/3`

= 10