Chapter 9, Problem 4RCC

(a)

To determine

To find:The vector $\text{u}$ in terms of $\text{i}$ and $\text{j}$ .

Answer to Problem 4RCC

The vector $\text{u}$ in terms of $\text{i}$ and $\text{j}$ is $\text{u}=u_1\text{i}+u_2\text{j}$ .

Explanation of Solution

Given information:

The given vector is $\text{u}=\left(u_1,u_2\right)$ .

Calculation:

The vector $\text{u}=\left(u_1,u_2\right)$ is in two dimensions, then vector $\text{u}$ in terms of $\text{i}$ and $\text{j}$ is.

$\text{u}=u_1\text{i}+u_2\text{j}$

Therefore, thevector $\text{u}$ in terms of $\text{i}$ and $\text{j}$ is $\text{u}=u_1\text{i}+u_2\text{j}$ .

(b)

To determine

To find:The vector $\text{v}$ in terms of $\text{i}$ , $\text{j}$ and $\text{k}$ .

Answer to Problem 4RCC

The vector $\text{v}$ in terms of $\text{i}$ , $\text{j}$ and $\text{k}$ is $\text{v}=\text{vi}+v_2{\text{j+v}}_3\text{k}$ .

Explanation of Solution

Given information:

The given vector is $\text{v}=\left(v_1,v_2,v_3\right)$ .

Calculation:

The vector $\text{u}=\left(u_1,u_2\right)$ is in two dimensions, then vector $\text{v}$ in terms of $\text{i}$ , $\text{j}$ and $\text{k}$ .

$\text{v}=\text{vi}+v_2{\text{j+v}}_3\text{k}$

Therefore, the vector $\text{v}$ in terms of $\text{i}$ , $\text{j}$ and $\text{k}$ is $\text{v}=\text{vi}+v_2{\text{j+v}}_3\text{k}$ .