Two perpendicular vectors, $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ , are added together giving vector $\overrightarrow { \mathrm { C } }$ . If the magnitudes of both vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ 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.

Question

Quizplus · Accepted Answer

When the magnitudes of $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ are doubled, the magnitude of $\overrightarrow { \mathrm { C } }$ will also double because $\overrightarrow { \mathrm { C } }$ is the resultant of two perpendicular vectors.

Two Perpendicular Vectors A→\overrightarrow { \mathrm { A } }A And B→\overrightarrow { \mathrm { B } }B

Two Perpendicular Vectors $\overrightarrow { \mathrm { A } }$ And $\overrightarrow { \mathrm { B } }$