Chapter 6, Problem 33CLT

To determine

The vector as a linear combination of the standard unit vectors iand j.

Answer to Problem 33CLT

The vector as a linear combination of the standard unit vectors iand j is $v=7i+8j$

Explanation of Solution

Given info:

Initail point : $(-1,2)$

Terminal point : $(6,10)$

Formula used:

A vector whose initial point is the origin $(0,0)$ can be uniquely represented by thecoordinates of its terminal point $(v_1,v_2)$ . This is the component form of a vector v,written as $v=\langle v_1,v_2\rangle$

Magnitude of $v=\sqrt{v_1{}^2+v_2{}^2}$

Calculation:

We have

Initail point : $(-1,2)$

Terminal point : $(6,10)$

So,

  $\begin{array}{l}v=\langle 6-\left(-1\right),10-2\rangle =\langle 7,8\rangle \\ v=7i+8j\end{array}$

Thevector as a linear combination of the standard unit vectors iand j is $v=7i+8j$

Conclusion:

Thus,thevector as a linear combination of the standard unit vectors iand j is $v=7i+8j$