Addition of vectors is governed by Parallelogram law of vectors but not by simple algebraic addition. Vectors and are places with their tails at a point without changing their directions. Considering them as two adjacent sides of a parallelogram, the diagonal from the tails is drawn. The diagonal gives the sum of the two vectors. Depending on the directions and magnitudes of two vectors, the length of its diagonal can be

Greater than or less than the magnitude of vector , hence option A is false

Equal to or less than the sum of magnitudes of and , hence option C is false

Equal to the sum of magnitudes of and if A and B are collinear and having the same direction, hence option D is false.

It is always possible to have | and , hence option B is true.