Question

Find the vector projection w of u = i – 6j onto v = 2i + 7j.

Answer 1

Given:

`u=i-6j\text{ }onto\text{ }v=2i+7j.`

To find:

The vector projection u onto v.

Step-by-step explanation:

The vector projection u onto v formula is,

`\frac{\vec{u}\cdot\vec{v}}{|\vec{v}|^2}\cdot\vec{v}`

Substituting the given values we get,

`\begin{gathered} ((i-6j)\cdot(2i+7j))/(|2i+7j|)(2i+7j)=((2-42))/((√(2^2+7^2))^2)(2\imaginaryI+7j) \\ =((2-42))/((√(4+49))^2)(2\mathrm{i}+7j) \\ =(-40)/((√(53))^2)(2\mathrm{i}+7j) \\ =(-40)/(53)(2\mathrm{i}+7j) \end{gathered}`

Final answer:

The vector projection u onto v is,

`(-40)/(53)(2\imaginaryI+7j)`