Question

In Exercises 24-27, find ${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}\mathbf{},{\mathrm{proj}}_{\mathbf{u}}\mathbf{v}$and the component of v orthogonal tou.

Short answer

The values are${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=0,{\mathrm{proj}}_{\mathbf{u}}\mathbf{}\mathbf{v}=0$ and the component of v orthogonal tou is.

Step-by-step solution

Step 1. Given information.

The given vectors are:

Step 2. Find the component of the projection of v onto u.

Then,

$$\begin{gathered} {\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=\frac{\mathit{u}\mathbf{·}\mathit{v}}{||\mathit{u}||} \\ =\frac{0}{\sqrt{14}} \\ =0 \end{gathered}$$

Therefore,${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=0$.

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

Therefore, the vector projection of v onto uis${\mathrm{proj}}_{\mathbf{u}}\mathbf{}\mathbf{v}=0$

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.