Chapter 11.2, Problem 20E

(a)

To determine

To Find:Component form of $u-v$ .

Answer to Problem 20E

The required component of the vector is $\left(5,-7\right)$ .

Explanation of Solution

Given Information:

  $\begin{array}{l}u=\left(3,-2\right)\\ v=\left(-2,5\right)\end{array}$

Calculation:

Component form of the vector is

  $\begin{array}{l}u-v\\ \text{=}\left(3-\left(-2\right),-2-5\right)\\ =\left(5,-7\right)\end{array}$

Conclusion:

Hence, the required component of the vector is $\left(5,-7\right)$ .

(b)

To determine

To Find: The magnitude of $u-v$ .

Answer to Problem 20E

The required magnitude of the vector is $\left|v\right|=\sqrt{74}$ .

Explanation of Solution

Given Information:

  $\begin{array}{l}u=\left(3,-2\right)\\ v=\left(-2,5\right)\end{array}$

Component of $u-v$ is $\left(5,-7\right)$

Formula Used:

Magnitude formula

  $\left|v\right|=\sqrt{a^2+b^2}$  ........ (1)

Here, $a$ and $b$ are two points.

Calculation:

Substitute $5,-7$ for $a,b$ in equation (1)

  $\begin{array}{c}\left|v\right|=\sqrt{{\left(5\right)}^2+{\left(-7\right)}^2}\\ =\sqrt{74}\end{array}$

Conclusion:

Hence, the required magnitude of the vector is $\left|v\right|=\sqrt{74}$ .