Chapter 9, Problem 61RE

To determine

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

  $4v-3w$

Answer to Problem 61RE

The value of the vector is $-20i+13j$ .

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

Calculation:

Consider the vectors:

  $v=-2i+j$ and $w=4i-3j$

Put the value of the vectors in the given expression $4v-3w$ .

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

With the help of additivity of vectors:

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

  $\begin{array}{c}4v-3w=4\left(-2i+j\right)-3\left(4i-3j\right)\\ =-8i+4j-12i+9j\\ =-20i+13j\end{array}$

Thus, the value of the addition of vectors are $-20i+13j$ .