b
(b) \(|\overrightarrow {\rm A} |\, = \,\sqrt {{2^2} + {3^2} + {{( - 1)}^2}} \)\( = \sqrt {4 + 9 + 1} \) \( = \sqrt {14} \)

\(|\overrightarrow B |\, = \,\sqrt {{{( - 1)}^2} + {3^2} + {4^2}} \) \( = \sqrt {1 + 9 + 16} \) \( = \sqrt {26} \)

\(\overrightarrow A \,.\,\overrightarrow B = \,2\,( - 1) + 3 \times 3 + ( - 1)\,(4) = 3\)

The projection of \(\overrightarrow A \,\,{\rm{on}}\,\overrightarrow B \) \( = \frac{{\overrightarrow A \,.\,\overrightarrow B }}{{|\overrightarrow B |}}\) \( = \frac{3}{{\sqrt {26} }}\)