Chapter 6.3, Problem 123E

To determine

To explain:

The error in the component form of the given vector $v$ solving method

Answer to Problem 123E

The component vector in the given solving is calculated by using the formula $v=\langle p_1-q_1,p_2-q_2\rangle$ is error. The component form of vector $v$ is $v=\langle 3,-5\rangle$ .

Explanation of Solution

Given information:

Initial point: $\left(-3,4\right)$

Terminal point: $\left(6,-1\right)$

Calculation:

The components of the vector $v$ are given as:

  $\begin{array}{l}{u}_1=-3-6=-9\\ u_2=4-\left(-1\right)=5\\ u=\langle -9,5\rangle \end{array}$

The vector initial point and terminal point is $\left(p_1,p_2\right)=\left(-3,4\right)$ and $\left(q_1,q_2\right)=\left(6,-1\right)$ respectively.

The component vector is calculated as $v=\langle q_1-p_1,q_2-p_2\rangle$ . But in the given solving method of component vector is calculated as $v=\langle p_1-q_1,p_2-q_2\rangle$ which is error. Due to wrong formula used, the wrong values of component vector are resulted.

The correct method to calculate component vector is:

  $\begin{array}{l}v=\langle q_1-p_1,q_2-p_2\rangle \\ v=\langle 6-\left(-3\right),-1-4\rangle \\ v=\langle 3,-5\rangle \end{array}$