Chapter 9, Problem 63RE

To determine

To calculate: To use the vectors $v=-2i+j$ and $w=4i-3j$ to find,

  $\Vert v\Vert$

Answer to Problem 63RE

The value of the vector is $\sqrt{5}$ .

Explanation of Solution

Given information:

The vectors:

  $v=-2i+j$ and $w=4i-3j$

Formula used:

For the vectors by the additivity of $a+b$ in these components of ‘i’ added to ‘i’ and components of ‘j’ added to ‘j’,

Such as, $\left(a_{1}i+b_{1}j\right)+\left(a_{2}i+b_{2}j\right)=\left(a_{1}i+a_{2}i\right)+\left(b_{1}j+b_{2}j\right)$ .

The magnitude of $\Vert v\Vert$ is find by the help of formula:

  $\Vert v\Vert =\sqrt{a^2+b^2}$

Calculation:

Consider the vectors:

  $v=-2i+j$ and $w=4i-3j$

Put the value of the vectors in the given expression $\Vert v\Vert$ .

Now $v=-2i+j$ and $w=4i-3j$ .

With the help of magnitude of vectors formula:

  $\Vert v\Vert =\sqrt{a^2+b^2}$

  $\Vert v\Vert =\Vert -2i+j\Vert$

Now find the magnitude of $v$ with the help of the given formula $\Vert v\Vert =\sqrt{a^2+b^2}$ .

  $\begin{array}{l}\Vert v\Vert =\sqrt{a^2+b^2}\\ \Vert v\Vert =\sqrt{{\left(-2\right)}^2+{\left(1\right)}^2}\\ \Vert v\Vert =\sqrt{4+1}\\ \Vert v\Vert =\sqrt{5}\end{array}$

Thus, the value of the magnitude of vectors are $\sqrt{5}$ .