The position vector of vertices A, B, C of Δ are i + 2j + 3k, i + j + 3k, 2i + j + 3k respectively.

Question

The position vector of vertices A, B, C of Δ are \(\hat i + 2\hat j + 3\hat k, \hat i + \hat j + 3\hat k, 2\hat i + \hat j + 3\hat k\) respectively. Let l is the length of angle bisector of ∠BAC, then the value of l² is

(1) \(4 + 2\sqrt 2\)

(2) \(4 - 2\sqrt 2\)

(3) \(2+ 2\sqrt 2\)

(4) \(2- 2\sqrt 2\)

Answer 1

Correct option is (2) \(4 - 2\sqrt 2\)