Chapter 6, Problem 33RE

To determine

To find: The component form and the magnitude of the given vector.

Answer to Problem 33RE

The component form of the vector $v$ is $\langle 7,-7\rangle$ and the magnitude is $9.899$ .

Explanation of Solution

Given information:

The initial point of the vector is $\left(0,10\right)$ and the terminal point is $\left(7,3\right)$ .

The component form of the vector $v$ is calculated as,

  $\begin{array}{c}v=\langle 7-\left(0\right),3-10\rangle \\ =\langle 7,-7\rangle \end{array}$

The magnitude of the vector $v$ is calculated as,

  $\begin{array}{c}\Vert v\Vert =\sqrt{7^2+{\left(-7\right)}^2}\\ =9.899\end{array}$

Therefore, the component form of the vector $v$ is $\langle 7,-7\rangle$ and the magnitude is $9.899$ .