1)

The position vector of A and B are 2ˆi+2ˆj+ˆk and 2ˆi+4ˆj+4ˆk. The length of the internal bisector of <BOA triangle AOB is


A) 1369

B) 1369

C) 203

D) 2179

Answer:

Option A

Explanation:

We have,

OA = |2ˆi+2ˆj+ˆk| = 3;

OB = |2ˆi+4ˆj+4ˆk| = 6

Since the internal bisector divides opposite side in the

1832021593_471251_37385_ans.png

ratio of adjacent sides

ACBC=36=12

where OD is the bisector of <BOA .

.'. The position vector of C is

2(2ˆi+2ˆj+ˆk)+(2ˆi+4ˆj+4ˆk)2+1

=2ˆi+83ˆj+2ˆk

.'. OD = |2ˆi+83ˆj+2ˆk|

= 1369