|
58 | 58 | be (0, 2, 4); the X component is 0, the Y component is 2, and the Z component is 4. When |
59 | 59 | writing them as part of an equation, they are written as follows:</para> |
60 | 60 | <informalequation> |
61 | | - <mediaobject> |
62 | | - <imageobject> |
63 | | - <imagedata fileref="ColumnVector.svg"/> |
64 | | - </imageobject> |
65 | | - </mediaobject> |
| 61 | + <xi:include href="ColumnVector.mathml" /> |
66 | 62 | </informalequation> |
67 | 63 | <para>In math equations, vector variables are either in boldface or written with an arrow |
68 | 64 | over them.</para> |
|
102 | 98 | components:</para> |
103 | 99 | <equation> |
104 | 100 | <title>Vector Addition with Numbers</title> |
105 | | - <mediaobject> |
106 | | - <imageobject> |
107 | | - <imagedata fileref="VectorAdditionNum.svg"/> |
108 | | - </imageobject> |
109 | | - </mediaobject> |
| 101 | + <xi:include href="VectorAdditionNum.mathml" /> |
110 | 102 | </equation> |
111 | 103 | <para>Any operation where you perform an operation on each component of a vector is |
112 | 104 | called a <glossterm>component-wise operation</glossterm>. Vector addition is |
|
127 | 119 | <para>Numerically, this means negating each component of the vector.</para> |
128 | 120 | <equation> |
129 | 121 | <title>Vector Negation</title> |
130 | | - <mediaobject> |
131 | | - <imageobject> |
132 | | - <imagedata fileref="VectorNegationNum.svg"/> |
133 | | - </imageobject> |
134 | | - </mediaobject> |
| 122 | + <xi:include href="VectorNegationNum.mathml" /> |
135 | 123 | </equation> |
136 | 124 | <para>Just as with scalar math, vector subtraction is the same as addition with the |
137 | 125 | negation of the second vector.</para> |
|
154 | 142 | vector addition.</para> |
155 | 143 | <equation> |
156 | 144 | <title>Vector Multiplication</title> |
157 | | - <mediaobject> |
158 | | - <imageobject> |
159 | | - <imagedata fileref="VectorMultiplicationNum.svg"/> |
160 | | - </imageobject> |
161 | | - </mediaobject> |
| 145 | + <xi:include href="VectorMultiplicationNum.mathml" /> |
162 | 146 | </equation> |
163 | 147 | <formalpara> |
164 | 148 | <title>Vector/Scalar Operations</title> |
|
178 | 162 | vector is multiplied with each component of the scalar.</para> |
179 | 163 | <equation> |
180 | 164 | <title>Vector-Scalar Multiplication</title> |
181 | | - <mediaobject> |
182 | | - <imageobject> |
183 | | - <imagedata fileref="VectorScalarMultNum.svg"/> |
184 | | - </imageobject> |
185 | | - </mediaobject> |
| 165 | + <xi:include href="VectorScalarMultNum.mathml" /> |
186 | 166 | </equation> |
187 | 167 | <para>Scalars can also be added to vectors. This, like vector-to-vector multiplication, has |
188 | 168 | no geometric representation. It is a component-wise addition of the scalar with each |
189 | 169 | component of the vector.</para> |
190 | 170 | <equation> |
191 | 171 | <title>Vector-Scalar Addition</title> |
192 | | - <mediaobject> |
193 | | - <imageobject> |
194 | | - <imagedata fileref="VectorScalarAddNum.svg"/> |
195 | | - </imageobject> |
196 | | - </mediaobject> |
| 172 | + <xi:include href="VectorScalarAddNum.mathml" /> |
197 | 173 | </equation> |
198 | 174 | <formalpara> |
199 | 175 | <title>Vector Algebra</title> |
|
204 | 180 | and multiplication. They are commutative, associative, and distributive.</para> |
205 | 181 | <equation> |
206 | 182 | <title>Vector Algebra</title> |
207 | | - <mediaobject> |
208 | | - <imageobject> |
209 | | - <imagedata fileref="VectorMathProperties.svg"/> |
210 | | - </imageobject> |
211 | | - </mediaobject> |
| 183 | + <xi:include href="VectorMathProperties.mathml" /> |
212 | 184 | </equation> |
213 | 185 | <para>Vector/scalar operations have similar properties.</para> |
214 | 186 | <formalpara> |
|
219 | 191 | <para>Numerically, computing the distance requires this equation:</para> |
220 | 192 | <equation> |
221 | 193 | <title>Vector Length</title> |
222 | | - <mediaobject> |
223 | | - <imageobject> |
224 | | - <imagedata fileref="VectorLengthNum.svg"/> |
225 | | - </imageobject> |
226 | | - </mediaobject> |
| 194 | + <xi:include href="VectorLengthNum.mathml" /> |
227 | 195 | </equation> |
228 | 196 | <para>This uses the Pythagorean theorem to compute the length of the vector. This works for |
229 | 197 | vectors of arbitrary dimensions, not just two or three.</para> |
|
239 | 207 | reciprocal of the length.</para> |
240 | 208 | <equation> |
241 | 209 | <title>Vector Normalization</title> |
242 | | - <mediaobject> |
243 | | - <imageobject> |
244 | | - <imagedata fileref="VectorNormalizationNum.svg"/> |
245 | | - </imageobject> |
246 | | - </mediaobject> |
| 210 | + <xi:include href="VectorNormalizationNum.mathml" /> |
247 | 211 | </equation> |
248 | 212 | <para>This is not all of the vector math that we will use in these tutorials. New vector |
249 | 213 | math operations will be introduced and explained as needed when they are first used. And |
|
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