If 4i + 7j + 8k, 2i + 3j+ 4k and 2i + 5j + 7k are the position vector of the vertices A,B and C respectively of triangle ABC. the position vector of the point where the bisector of angle A meets BC is
Answers
Answered by
11
Therefore the position vector of the point is and
Step-by-step explanation:
Given;
, and are the point vector of triangle 'ABC' and
The bisector of meets 'BC' which is known as 'D'
we know the angle bisector theorem,which states that,
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
So,
Now,
Vector P.V of - P.V of
Vector P.V of - P.V of
So as for,
We have,
So,
'D' divides the side BC in the ratio internally if 'AD' is the internal angle bisector. and externally if 'AD' is the external angle bisector.
So, position vector of 'D' can be obtained by using section formula;
P.V of and
P.V of and
P.V of and
So the position vector of the point is and
Similar questions