Given:
[tex]u=i-6j\text{ }onto\text{ }v=2i+7j.[/tex]To find:
The vector projection u onto v.
Explanation:
The vector projection u onto v formula is,
[tex]\frac{\vec{u}\cdot\vec{v}}{|\vec{v}|^2}\cdot\vec{v}[/tex]Substituting the given values we get,
[tex]\begin{gathered} \frac{(i-6j)\cdot(2i+7j)}{|2i+7j|}(2i+7j)=\frac{(2-42)}{(\sqrt{2^2+7^2})^2}(2\imaginaryI+7j) \\ =\frac{(2-42)}{(\sqrt{4+49})^2}(2\mathrm{i}+7j) \\ =\frac{-40}{(\sqrt{53})^2}(2\mathrm{i}+7j) \\ =\frac{-40}{53}(2\mathrm{i}+7j) \end{gathered}[/tex]Final answer:
The vector projection u onto v is,
[tex]\frac{-40}{53}(2\imaginaryI+7j)[/tex]