Chapter 6.3, Problem 66E

To determine

To Find:Linear combination of the standard unit vectors i and j.

Answer to Problem 66E

  $3i+8j$

Explanation of Solution

Given: The initial and the terminal points are given. Write the Linear combination of the standard unit vectors i and j.

  $\begin{array}{l}\text{Initial point:}(-1,-5)\\ \text{Terminal point:(2,3)}\end{array}$

Formula Used:

Component Form of the vector: $<q_1-p_1,q_2-p_2>=<v_1,v_2>=v$

  $\begin{array}{l}\text{Initial point:}(-1,-5)\\ \text{Terminal point:(2,3)}\end{array}$

Here

  $\begin{array}{l}{p}_1=-1,p_2=-5\\ q_1=2,q_2=3\end{array}$

Using the formula of component form,subtract the Initial point from the terminal point

We get

  $<2-(-1),3-(-5)>=<3,8>$

Thus

The linear combination of the vector is $3i+8j$ .

Hence, the Linear combination of the standard unit vectors i and j is $3i+8j$ .