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The vertices of a triangle are A(1,1,2),...

The vertices of a triangle are A(1,1,2), B (4,3,1) and C (2,3,5). The vector representing internal bisector of the angle A is

A

`hati+hatj+2hatk`

B

`2hati-2hatj+hatk`

C

`2hati+2hatj+hatk`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
From the figure, we have
`b=AC=hati+2hatj+3hatk`
and `c=AB=3hati+2hatj+hatk`

`therefore`Unit vector along the bisector of `angleA` is given by
`=(b+c)/(2)=((hati+2hatj+3hatk)+(3hati+2hatj-hatk))/(sqrt(14))`
`=(2hati+2hatj+hatk)/(sqrt(14))`
`therefore`Any vector along the angle bisector of
`angleA=2hati+2hatj+hatk`.
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Statement 1: If vec ua n d vec v are unit vectors inclined at an angle alphaa n d vec x is a unit vector bisecting the angle between them, then vec x=( vec u+ vec v)//(2sin(alpha//2)dot Statement 2: If "Delta"A B C is an isosceles triangle with A B=A C=1, then the vector representing the bisector of angel A is given by vec A D=( vec A B+ vec A C)//2.