Let $\vec { a } = 4 \hat { i } + 3 \hat { j }$ and $\vec { b } = 3 \hat { i } - 4 \hat { j } + 5 \hat { k }$ and $\overrightarrow { \mathrm { c } }$ is a vector such that $\vec { c } \cdot ( \vec { a } \times \vec { b } ) + 25 = 0 , \vec { c } \cdot ( \hat { i } + \hat { j } + \hat { k } ) = 4$ and projection of $\vec { c }$ on $\overrightarrow { \mathrm { a } }$ is 1 , then the projection of $\vec { c }$ on $\vec { b }$ equals:
(1) $\frac { 5 } { \sqrt { 2 } }$
(2) $\frac { 1 } { 5 }$
(3) $\frac { 1 } { \sqrt { 2 } }$
(4) $\frac { 3 } { \sqrt { 2 } }$