Home
Class 12
MATHS
A(1,-1,-3), B(2, 1,-2) & C(-5, 2,-6) are...

`A(1,-1,-3), B(2, 1,-2) & C(-5, 2,-6)` are the position vectors of the vertices of a triangle ABC. The length of the bisector of its internal angle at A is :

Text Solution

Verified by Experts

The correct Answer is:
3
We have, `AB=hati+2hatj+hatk,AC=-6hati+3hatj-3hatk`
`implies|AB|=sqrt(6) and |AC|=3sqrt(6)`
Clearly, point D divides BC in the ratio AB:AC, i.e., 1:3
`therefore`Position vector of `D=((-5hati+2hatj-6hatk)+3(2hati+hatj-2hatk))/(1+3)`
`=(1)/(4)(hati+5hat9-12hatk)`
`thereforeAD=(1)/(4)(hati+5hatj-12hatk)-(hati-hatj-3hatk)=(3)/(4)(-2hati+3hatj)`
`|AD|=AD=(3)/(4)sqrt(10)`
`therefore lamda=3`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Consider a triangular pyramid ABCD the position vectors of whone agular points are A(3,0,1),B(-1,4,1),C(5,3, 2) and D(0,-5,4) Let G be the point of intersection of the medians of the triangle BCD. The length of the vector bar(AG) is

A (1, -1, -3), B(2, 1, -2) and C(-5, 2, -6) are the verticies of DeltaABC . Find co-ordinates of point D, if bisector of angleA intersects bar(BC) at point D.

Let A(1, 2, 3), B(0, 0, 1) and C(-1, 1, 1) are the vertices of triangleABC . Q. The equation of internal angle bisector through A to side BC is

A(1, 1, 2), B(4, 3, 1) and C(2, 3, 5) are vertices of a triangle ABC. The vector along the bisector angleA is …………..

If 4hati+ 7hatj+ 8hatk, 2hati+ 3hatj+ 4hatk and 2hati+ 5hatj+7hatk are the position vectors of the vertices A, B and C, respectively, of triangle ABC, then the position vector of the point where the bisector of angle A meets BC is

If A(5,-1), B(-3,-2) and C(-1, 8) are the vertices of Delta ABC , find the length of median through A and the coordinates of the centroid

If A=(1, 2, 3), B=(4, 5, 6), C=(7, 8, 9) and D, E, F are the mid points of the triangle ABC, then find the centroid of the triangle DEF.

The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices of a parallelogram ABCD, then

If A(2, 2, -3), B(5, 6, 9) and C(2, 7, 9) be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D. Find the coordinates of D.

If A(2,2) , B(-4,-4) and C(5,-8) are the vertices of Delta ABC then the length of the median through C is . . . . . Units