In the Cartesian coordinate plane, vectors $\overrightarrow { \mathrm { u } _ { 1 } } = ( 3,4 )$ and $\overrightarrow { \mathrm { u } _ { 2 } } = ( 8 , - 6 )$ are given. For a vector $\vec { V }$ taken in this plane, the perpendicular projection vector onto the $\overrightarrow { u _ { 1 } }$ vector is 3 units, and the perpendicular projection vector onto the $\overrightarrow { u _ { 2 } }$ vector is 1 unit in length. Accordingly, what is the length of the $\vec { v }$ vector in units? A) $\sqrt { 5 }$ B) $\sqrt { 10 }$ C) $5 \sqrt { 5 }$ D) 5 E) 10
In the Cartesian coordinate plane, vectors $\overrightarrow { \mathrm { u } _ { 1 } } = ( 3,4 )$ and $\overrightarrow { \mathrm { u } _ { 2 } } = ( 8 , - 6 )$ are given. For a vector $\vec { V }$ taken in this plane, the perpendicular projection vector onto the $\overrightarrow { u _ { 1 } }$ vector is 3 units, and the perpendicular projection vector onto the $\overrightarrow { u _ { 2 } }$ vector is 1 unit in length.
Accordingly, what is the length of the $\vec { v }$ vector in units?
A) $\sqrt { 5 }$
B) $\sqrt { 10 }$
C) $5 \sqrt { 5 }$
D) 5
E) 10