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9.2 - Reading questions
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<h2>[9.2] - Reading Assignment
</h2>

<p class="show"><b>Read</b> section 9.2 in the textbook. Make sure you have a sense of the following terms and concepts (shown here for 2-dimensional vectors):<br>

[${}^*$ - means some part of this terminology may <i>not</i> be in the textbook]

<p><img src="../gco/0g/9.1.vector2d.jpg"><br>
In the diagram above...
<ul>
<li>$P_1$ is the <i>initial point</i> (tail)
and $P_2$ is the <i>terminal point</i> (head)
<li>The <b>components</b> of the vector $\myv{P_1P_2}$ are 
$$\langle \Delta x, \Delta y \rangle\equiv \langle x_2-x_1, y_2-y_1 \rangle.$$
<li>${}^*$
 Standard position means "tail at the origin".
The "position vector of a point" $B$ is a vector in standard position with its tip at $B$.
<li>${}^*$ Length of a vector $\equiv$
 magnitude $\equiv$ "measure" $\equiv$ "norm"
<li>Two vectors, $\myv a$ and $\myv b$ are <b>equivalent</b> or equal if they have the same length and the same direction.
<li>A unit vector always has a length of 1.  A unit vector parallel to $\myv u$and pointing in the same directions is $\uv u = \myv u / |\myv u|$.
</ul>





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<h3>[9.2] Reading questions</h3>
<ol class="todo">
<li><img src="../gco/0g/9.1.parallel.jpg" class="rightalign">
For the 2 vectors in the top diagram, which statement<b>s</b> are true? (Can be more than one.)<ol type='a'>
<li>They have the same direction.
<li>They have the same length.
<li>They are parallel to each other.
<li>They are equivalent vectors.
</ol>
<p class="justme result"><span class="answer">All</span> of these are true</p>
<li>For the 3 vectors in the bottom diagram, which statements are true?
<ol type='a'>
<li>They have the same direction.
<li>They have the same length.
<li>They are parallel to each other.
<li>They are equivalent vectors.
</ol>
<p class="justme result"><span class="answer">c.</span> They are parallel to each other.

<li>Sketch on the bottom diagram a <b>unit vector</b> which points in the same direction as the longest vector of the 3 shown.
<p class="justme result">
A unit vector has a length of 1.<br>
<img src="../gco/0g/9.7.unit.jpg">


<li>On the bottom diagram, indicate which of the vectors is a "position vector" for the point $(-3,1)$.
<p class="result">A position vector would have its tail at the origin, and its head at (-3,1).  So, <span class="answer">None of these is a position vector for $(-3,1)$</span>.

<li>If $\myv a=\langle a_1,a_2,a_3 \rangle$ has $a_2 \gt 0$ and $a_3\lt 0$,
    then is the $z$-component of $-3\myv a$ positive or negative?
<p class="result">The $z$ component of $\myv a$ is $a_3$.  The $z$ component of $-3\myv a$ is $-3a_3$.  If $a_3$ is negative, then <span class="answer">$-3a_3$ is positive</span>.  
<li>What's one or two "muddy points" in the reading that you'd like to clear up.  Or (if nothing seemed muddy) one thing that you *wonder* about.
</ol>




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