Let A \left(\right. 2 , 1 , - 3 \left.\right) and B \left(\right. 5 , - 8 , 3 \left.\right) be two given points. Find the coordinates of the points of trisection of the line segment A B.

Engineering

Mathematics

Line of Greatest Slope

Question

Let

A (2, 1, - 3)

and

B (5, - 8, 3)

be two given points. Find the coordinates of the points of trisection of the line segment

A B

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Given : Point

A (2, 1, - 3)

and

B (5, - 8, 3)

m = 2

and

n = 1

To Find :- Co-ordinate of point C which intersect trisection of the segment

A B

Solution

Using section Formula:

C = \frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}, \frac{m z_{2} + n z_{1}}{m + n}

= \frac{2 \times 5 + 1 \times 2}{3}, \frac{2 \times - 8 + 1 \times 1}{3}, \frac{2 \times 3 + 1 \times - 3}{3}

= \frac{12}{3}, \frac{- 15}{3}, \frac{3}{3}

= 4, - 5, 1

Hence

Therefore

(4, - 5, 1)

is the point of trisection of the segment

A B

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