Answer
Yes. The sum of the magnitudes of two vectors can equal the magnitude of the sums of those vectors. It happens when they are parallel to each other ( angle between them is 0 degree)
Work Step by Step
Magnitude of vector A+ magnitude of Vector B = Magnitude of vector [A+B]
Let for the above condition the angle between vectors be \theta
$A + B$ = $ \ sqrt [Ax^{y}2+ Bx^{y}2+ 2A B cos\theta$ [ Law of parallelogram]
Squaring both sides we get
==> $[A+B]x^{y}2=Ax^{y}2+Bx^{y}2+2 A B COS\theta$
==> $Ax^{y}2+Bx^{y}2+2 A B = Ax^{y}2+Bx^{y}2+2 A B COS\theta$
==> $2 A B = 2 A B COS \theta$
==> $COS \theta=1$
==> $\theta=0 DEGREE$
This can only occur when both the vectors are acting in same direction.
