Two Perpendicular Vectors $\vec { A }$ And $\overrightarrow { \mathbf { B } }$

Multiple Choice

Two perpendicular vectors, $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ , are added together giving vector $\overrightarrow { \mathrm { C } }$ . If the magnitudes of both vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ are doubled without changing their directions, the magnitude of vector $\overrightarrow { \mathrm { C } }$ will

A) increase by a factor of 8.
B) increase by a factor of 4.
C) increase by a factor of 2.
D) increase by a factor of $\sqrt { 2 }$ .
E) not change.