Chapter 6.3, Problem 106E

a.

To determine

Verify that is $a=-d$ true or false.

Answer to Problem 106E

  $\boxed{true}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

The vectors $a,d$ are equal in magnitude and opposite in direction

Hence, $a=-d$ is $\boxed{true}$

b.

To determine

Verify that $c=s$ is true or false.

Answer to Problem 106E

  $\boxed{true}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

The vectors $c,s$ are equal in magnitude and same in direction

Hence $c=s$ is $\boxed{true}$

c.

To determine

Verify that $a+u=c$ is true or false.

Answer to Problem 106E

  $\boxed{true}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

The vectors $a,u$ are adjacent vectors of a square

So its diagonal vector $c$ is a resultant of $a,u$

Hence, $a+u=c$ is $\boxed{true}$

d.

To determine

Verify that $v+w=-s$ is true or false.

Answer to Problem 106E

  $\boxed{false}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

The vectors $v,s,-w$ completes a triangle

That is $v+s-w=0\to v-w=-s$

Hence, $v+w=-s$ is $\boxed{false}$

e.

To determine

Verify that $a+w=-2d$ is true or false.

Answer to Problem 106E

  $\boxed{true}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

The vectors $a,d$ are equal to in the magnitude and opposite in direction

And $a,w$ are equal vectors

Hence,

  $\begin{array}{l}a+w=-d-d\\ =-2d\end{array}$

Hence, $a+w=-2d$ is $\boxed{true}$

f.

To determine

Verify that $a+d=0$ is true or false.

Answer to Problem 106E

  $\boxed{true}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

From (a) $a=-d\to a+d=0$

Hence, $a+d=0$ is $\boxed{true}$

g.

To determine

Verify that $u-v=-2(b+t)$ is true or false.

Answer to Problem 106E

  $\boxed{false}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

From the figure $u=-b,v=t$

  $\begin{array}{l}u-v=-b-t\\ =-\left(b+t\right)\end{array}$

Therefore $u-v=-\left(b+t\right)$

Hence $u-v=-2(b+t)$ is $\boxed{false}$

h.

To determine

Verify that $t-w=b-a$ is true or false.

Answer to Problem 106E

  $\boxed{true}$

Explanation of Solution

Given information:

Use the figure to determine whether each statement is true or false. Justify your answer.

  

Calculation:

From the figure $t=b,w=a$

  $t-w=b-a$

Hence $t-w=b-a$ is $\boxed{true}$