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<!DOCTYPE html>
<html data-require="math math-format graphie">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Adding vectors</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars" data-ensure="0 < abs( AX + BX ) && abs( AX + BX ) < 10 && 0 < abs( AY + BY ) && abs( AY + BY ) < 10 && (AX * AY) * (BX * BY) < 0">
<var id="AX">randRangeNonZero( -9, 9 )</var>
<var id="AY">randRangeNonZero( -9, 9 )</var>
<var id="BX">randRangeNonZero( -9, 9 )</var>
<var id="BY">randRangeNonZero( -9, 9 )</var>
</div>
<div class="problems">
<div>
<div class="question">
<div id="graph" class="graphie" style="float: right">
graphInit({
range: 10,
scale: 20,
tickStep: 1,
labelStep: 1,
unityLabels: false,
labelFormat: function( s ) { return "\\small{" + s + "}"; },
axisArrows: "<->"
});
line( [0, 0], [AX, AY], { stroke: "#6495ed", arrows: "->" } );
line( [0, 0], [BX, BY], { stroke: "#28ae7b", arrows: "->" } );
var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY );
label( [AF * AX, AF * AY], "\\vec a", { color: "#6495ed" } );
var BF = 1 + 0.8 / sqrt( BX * BX + BY * BY );
label( [BF * BX, BF * BY], "\\vec b", { color: "#28ae7b" } );
</div>
<p>What is <code>\vec a + \vec b</code>?</p>
<p><code>\begin{align*}
\vec a &= <var>AX</var> \hat\imath + <var>AY</var> \hat\jmath \\
\vec b &= <var>BX</var> \hat\imath + <var>BY</var> \hat\jmath
\end{align*}</code></p>
</div>
<div class="solution" data-type="multiple">
<p><span class="sol" data-fallback="1"><var>AX + BX</var></span> <code>\hat\imath + {}</code><span class="sol" data-fallback="1"><var>AY + BY</var></span> <code>\hat\jmath</code></p>
</div>
</div>
</div>
<div class="hints">
<p>Sum the <code>\hat\imath</code> and <code>\hat\jmath</code> components separately.</p>
<div>
<p><code>\hat a + \hat b = (<var>AX</var> + <var>BX</var>) \hat\imath + (<var>AY</var> + <var>BY</var>) \hat\jmath</code></p>
<div class="graphie" data-update="graph">
line( [BX, BY], [BX + AX, BY + AY], { stroke: "#6495ed", arrows: "->" } );
</div>
</div>
<div>
<p><code>\hphantom{\hat a + \hat b} = <var>AX + BX</var>\hat\imath + <var>AY + BY</var>\hat\jmath</code></p>
<div class="graphie" data-update="graph">
line( [0, 0], [BX + AX, BY + AY], { stroke: "#ffa500", arrows: "->" } );
</div>
</div>
</div>
</div>
</body>
</html>
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