It is given that,
[tex]\begin{gathered} u\text{ = }\langle\text{ 1, 6 }\rangle \\ v\text{ = }\langle\text{ 4, -9 }\rangle \\ \parallel\bar{v}\parallel\text{ = }\sqrt{\left(4\right)^2}\text{ + \lparen-9\rparen}^2 \\ \parallel\bar{v}\parallel\text{ = }\sqrt{16+81} \\ \parallel\bar{v}\parallel\text{ = }\sqrt{97} \end{gathered}[/tex]Calculating the dot product.
[tex]\begin{gathered} \bar{u}\bar{.v}=\text{ }\langle1,6\rangle\text{ . }\langle4,-9\rangle \\ \bar{u}\bar{.v}=\text{ 4 - 54} \\ \bar{u}\bar{.v}=\text{ 50} \end{gathered}[/tex]Scalar projection u onto v is given as,
[tex]\begin{gathered} Scalar\text{ projection = }\frac{\bar{u}.\bar{v}}{\parallel\bar{v}\parallel} \\ Scalar\text{ projection =}\frac{50}{\sqrt{97}} \\ Scalar\text{ projection = }\frac{50}{9.85} \\ Scalar\text{ projection = 5.076} \\ \end{gathered}[/tex]Vector projection of u onto v is calculated as,
[tex]Vector\text{ projection = }\frac{\bar{u}\bar{.v}}{\parallel v\parallel^2}\bar{\text{ v}}[/tex]Therefore,
[tex]\begin{gathered} Vector\text{ projection = }\frac{50}{(\sqrt{97})^2}\text{ }\times\bar{\text{ v}} \\ Vector\text{ projection = }\frac{50}{(97)}\text{ }\times\bar{\text{ v}} \\ Vector\bar{\text{ projection = 0.5155}}\bar{\text{ v}} \end{gathered}[/tex]Thus the required answer is,
[tex]\begin{gathered} Scalar\text{ projection = 5.076} \\ Vector\bar{\text{ projection = 0.5155 }}\bar{.v} \end{gathered}[/tex]