Chapter 8.2, Problem 40E

To determine

To find: the magnitude of the vector and also write the vector as a sum of unit vectors.

Answer to Problem 40E

  $\begin{array}{l}\text{Magnitude}=\sqrt{17}\\ \text{Sum of unit vector}=-4\overrightarrow{i}+\overrightarrow{j}\end{array}$

Explanation of Solution

Given information:

The ordered pair of the vector is $\langle -4,1\rangle$ .

Calculation:

The magnitude of the vector can be evaluated as follows:

  $\begin{array}{c}\text{Magnitude of vector}=\sqrt{{\left(x\right)}^2+{\left(y\right)}^2}\\ =\sqrt{{\left(-4\right)}^2+{\left(1\right)}^2}\left[\text{Put ordered pairs of the vector}\right]\\ =\sqrt{16+1}\\ =\sqrt{17}\end{array}$

Thus the magnitude of the vector is $\sqrt{17}$ .

The sum of unit vector can be evaluated as follows:

  $\begin{array}{c}\text{Sum of unit vector}=x\overrightarrow{i}+y\overrightarrow{j}\\ =-4\overrightarrow{i}+\left(1\right)\overrightarrow{j}\left[\text{Put the value of ordered pairs}\right]\\ =-4\overrightarrow{i}+\overrightarrow{j}\end{array}$

Thus the sum unit of vector is $-4\overrightarrow{i}+\overrightarrow{j}$ .