distance between A and B

Question

let the angle b/n v= -2i-j+2k and AB be 60 degree, where A and B are points in space. if V.AB=2 then what is the distance between A and B?

Answer 1

v= -2i-j+2k and AB be 60, A and B are position vectors

|v| = sqrt( 4 + 1 + 4 ) = 3

v.AB = 2 (  v.AB is dot product of v and AB )

|v|. |AB| cos 60 = 2

3 . |AB| .( ½) = 2

|AB| =  4/3