Engineering
Mathematics
Line of Greatest Slope
Question
If A(2,2,3),B(5,6,9),C(2,7,9) be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D, then find the coordinates of D.
(132,72,9)
(72,132,9)
(92,72,9)
(132,92,9)
JEE Advance
College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Solution
Verified BY
Verified by Zigyan

We have,

Point

A(x1,y1,z1)=(2,2,3)

B(x2,y2,z2)=(5,6,9)

C(x3,y3,z3)=(2,7,9)

Let the coordinates of point D(x,y,z).

So,

According to question,

AB=(52)2+(62)2+(93)2

AB=9+16+149=132=13

AC=(22)2+(72)2+(9+3)2

AC=0+25+144=169=13

Thus ABC is isosceles triangle with AB=AC

So, angle bisector AD bisects BC

D(5+22,6+72,9+92)(72,132,9)

Hence, this is the ansewr.
Lock Image

Please subscribe our Youtube channel to unlock this solution.