Question

In Exercises 24-27, find comp_uv, proj_uv, and the component of v orthogonal tou.

Short answer

The values are and the component of v orthogonal tou is.

Step-by-step solution

Step 1. Given information.

The given vectors are:

Step 2. Find compu v.

${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=\frac{\mathit{u}\mathbf{·}\mathit{v}}{||\mathit{u}||}$is the projection of vonto u.

then, localid="1649668447466" ${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=\frac{\mathit{u}\mathbf{·}\mathit{v}}{||\mathit{u}||}$is:

localid="1649667564938" $=\frac{13}{\sqrt{5}}$

Step 3. Find the vector projection of v onto u.

Step 4. Find the component of v orthogonal to u.

The component of v orthogonal tou is$\mathbf{v}-{\mathrm{proj}}_{\mathbf{u}}\mathbf{v}$.

Therefore, the component of v orthogonal to u is localid="1649668403950" .