Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. PointParallel tov=(0, 0, 0)&lt;&lt;8, 1, 4&gt;&gt; (a) parametric equations (b) symmetric equations 8x=y=4z 4x=y=8z x8=y=z4 x4=y=z8

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Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line.  PointParallel tov=(0, 0, 0)&amp;lt;&amp;lt;8, 1, 4&amp;gt;&amp;gt;  (a) parametric equations  (b) symmetric equations  8x=y=4z  4x=y=8z  x8=y=z4  x4=y=z8

Richard Cheatham · Accepted Answer

Step 1  consider the t equation  Point =(0, 0, 0)  v=(8, 1, 4)  Step 2  Sets of parametric equations and symmetric equations of the line that passes through the given point   Point =(0, 0, 0)  v=(8, 1, 4)  To find a set of parametric equations of the line, we use the coordinates:  x1=0  y1=0  z1=0  The direction numbers:  a=8, b=1, c=4  The parametric equations are:  x=0+8=8  y=0+1=1  z=0+4=4  (b) symmetric equation for  8x=y=4z  x−x1a=y−y1b=z−z1c  Substitute (x, y, z)=(0, 0, 0)n=⟨a, b, c⟩=⟨8, 1, 4⟩  in symmetric equation  x−08=y−01=z−34  8−80=y−01=4−34  88=y−01=14  Direction number as integers 1, 1, 4.  symmetric equation for 4x=y−8Z  substitute (x, y, z)=(0, 0, 0)n=⟨a, b, c⟩=⟨8, 1, 4⟩x−08=y−01=z−34  in symmetric equation 0−88=0−01=4−34  4−08=0−01=8−44 direction number as integer 1, 1, 4  48=01=44  Direction number as integer 2, 1, 1

Find sets of parametric equations and symmetric equations of the

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