Chapter 8.7, Problem 41PPS

a.

To determine

Draw a vector in coordinate plane as initial point is origin.

Answer to Problem 41PPS

  

Explanation of Solution

Given information:

Initial point $A$ and terminal point $B$ . Length of $\stackrel{\rightharpoonup }{AC}$ is twice the $\stackrel{\rightharpoonup }{AB}$ with same direction.

Calculation:

Let draw the vector as per given infirmation,

  

Hence, the vector drawn.

b.

To determine

Draw a vector in coordinate plane as initial point is origin.

Answer to Problem 41PPS

  

Explanation of Solution

Given information:

  $\stackrel{\rightharpoonup }{DE}$ With point $D$ located at the origin and $\stackrel{\rightharpoonup }{DF}$ three times as long as $\stackrel{\rightharpoonup }{DE}$ in same direction. $\stackrel{\rightharpoonup }{GH}$ with point $G$ located at the origin and $\stackrel{\rightharpoonup }{GJ}$ four times as long as $\stackrel{\rightharpoonup }{GH}$ in same direction.

Calculation:

Let draw the vector as per given infirmation,

  

Hence, the vector drawn.

c.

To determine

Complete the table.

Answer to Problem 41PPS

  $\begin{array}{l}CoordinateScalerQuantity\\ \begin{array}{ccccc}B& \left(2,3\right)& C& \left(4,6\right)& 2\\ E& \left(1,3\right)& F& 3,9& 3\\ H& \left(-2,0\right)& J& \left(-8,0\right)& 4\end{array}\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}CoordinateScalerQuantity\\ \begin{array}{ccccc}B& & C& & \\ E& & F& & \\ H& & J& & \end{array}\end{array}$

Calculation:

Refered the data given in part $ab$ we can complete the table,

  $\begin{array}{l}CoordinateScalerQuantity\\ \begin{array}{ccccc}B& \left(2,3\right)& C& \left(4,6\right)& 2\\ E& \left(1,3\right)& F& 3,9& 3\\ H& \left(-2,0\right)& J& \left(-8,0\right)& 4\end{array}\end{array}$

d.

To determine

Make a conjecture about the relationship.

Answer to Problem 41PPS

Multiply the $xandy$ coordinate by the scalar quantity.

Explanation of Solution

Given information:

Relationship between coordinates of the terminal point of the initial vector and coordinates of terminal point of the vector that is incresed by a scalar quantity.

Calculation:

Multiply the $xandy$ coordinate by the scalar quantity.

e.

To determine

Write an algebraic expression for the terminal point of new vector.

Answer to Problem 41PPS

  $\left(kx,ky\right)$

Explanation of Solution

Given information:

Vector terminal point $\left(x,y\right)$ and it is multiplied by a scalar quantity $k$ .

Calculation:

An algebraic expression for the terminal point of new vector,

Vector terminal point $\left(x,y\right)$ and it is multiplied by a scalar quantity $k$ .

  $\left(kx,ky\right)$