Question

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

• A. $\frac{\sqrt{10}}{4}$
• B. $\frac{3\sqrt{10}}{4}$
• C. $\sqrt{10}$
• D. none

Answer 1

The correct option is B $\frac{3\sqrt{10}}{4}$

$\frac{AB}{AC}=\frac{BE}{EC}$

$\frac{\sqrt{6}}{3\sqrt{6}}=\frac{BE}{EC}=\frac{1}{3}$

So point $E=(\frac{1}{4}+\frac{5}{4},-3)$

So $AE=\frac{3\sqrt{10}}{4}$