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If veca=hati+hatj+hatk & vecB=hati-hatj+...

If `veca=hati+hatj+hatk` & `vecB=hati-hatj+hatk` are the sides of AB & AC of `/_\ABC` if AD is the angle bisector of `angleBAC` where D lies on BC, then length of AD is

A

1

B

`sqrt2`

C

`sqrt3`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B

Let A is at origin then B(1,1,1) and C(1,-1,1) also `AB=sqrt(3)" "AC=sqrt(3)`
Hence bisector theorem
`(BD)/(DC)=(AB)/(AC)=1`
`therefore D(1,0,1)" "therefore AD=sqrt(1+0+1)=sqrt(2)`.
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