&nbsp;Find the parametric and symmetric equations of the line L that passes through the Point (2, −4, 8) and parallel to v = 〈1, 2, −2〉.&nbsp;

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&amp;nbsp;Find the parametric and symmetric equations of the line L that passes through the Point (2, −4, 8) and parallel to v = 〈1, 2, −2〉.&amp;nbsp;

karton · Accepted Answer

To find the parametric and symmetric equations of the line L that passes through the point (2, -4, 8) and is parallel to the vector 𝐯=⟨1,2,−2⟩, we can use the following formulas:1. Parametric equations:x=x0+aty=y0+btz=z0+ct2. Symmetric equations:x−x0a=y−y0b=z−z0cwhere (x0,y0,z0) is a point on the line, and a, b, and c are the direction ratios of the line.Given that the line is parallel to 𝐯=⟨1,2,−2⟩, we can assign the direction ratios as a=1, b=2, and c=−2.Using the point (2,−4,8) as the initial point (x0,y0,z0), we can substitute these values into the equations:1. Parametric equations:x=2+ty=−4+2tz=8−2t2. Symmetric equations:x−21=y+42=z−8−2Simplifying the symmetric equations, we get:x−2=y+42=8−z−2In summary, the parametric equations of the line L are:x=2+ty=−4+2tz=8−2tAnd the symmetric equations of the line L are:x−2=y+42=8−z−2

Find the parametric and symmetric equations of the

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