Only the Sum and the Difference Survived

VectorsMedium+20 XP+20

Only the Sum and the Difference Survived

A delivery drone flies exactly two legs, described by vectors $\vec{A}$ and $\vec{B}$ . Its flight recorder has a bug: instead of storing the legs themselves, it stored only their sum and their difference.

$\vec{A} + \vec{B} = (7,\ 1) \qquad\quad \vec{A} - \vec{B} = (1,\ 9)$

What is the magnitude of the second leg, $\|\vec{B}\|$ ?

Hints

Select all that apply.

Adding Vectors: Tip to Tail

Drag A and B. Place the second vector's tail at the first's tip — the resultant runs start to end.

Drag A or B

Component-wise

A = (3.0, 1.0)

B = (1.0, 3.0)

A + B = (4.0, 4.0)

Only the Sum and the Difference Survived