Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Show that the three points A (2, 3, 4), B (–1, 2, – 3) and C (– 4, 1, – 10) are collinear and find the ratio in which C divides AB.

Show that the three points A (2, 3, 4), B (–1, 2, – 3) and C (– 4, 1, – 10) are collinear and find the ratio in which C divides AB.

Answers (1)

Given:

A(2,3,4), B(-1,2,-3) & C(-4,1,-10)

Now,

AB = \sqrt{(2+1)^{2}+(3-2)^{2}+(4+3)^{2} }

                  = \sqrt{9+1+49 } = \sqrt{59 }

BC = \sqrt{(-1+4)^{2}+(2-1)^{2}+(-3+10)^{2}}

                  = \sqrt{9+1+49 } = \sqrt{59 }

AC = \sqrt{(2+4)^{2}+(3-1)^{2}+(4+10)^{2} }

                  = \sqrt{36+4+196 } = 2\sqrt{59}

Now, AB + BC = \sqrt{59}+\sqrt{59}

                  = 2\sqrt{59}

                  = AC

Thus, A,B & C are collinear.AC:BC = 2\sqrt{59}:\sqrt{59} = 2:1

Thus, C divides AB externally in the ratio 2:1.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question