How do you find parametric equations and symmetric equations for the line through #(3, −2, 5)# and parallel to the line #x + 3 = y/2 = z − 2#?

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Answer 1 · 2017-06-18T15:24:48

The symmetric form is:

#(x-x_0)/a=(y-y_0)/b=(z-z_0)/c#

The parametric forms are:

#x=at+x_0,y=bt+y_0, and z = ct+z_0#

Given: #x + 3 = y/2 = z − 2#

Rewrite in symmetric form:

#(x - (-3))/1 = (y- 0)/2 = (z − 2)/1#

Please observe that the current point is #(-3,0,2)#

Change to the #(3, -2, 5)#

#(x - 2)/1 = (y- (-2))/2 = (z − 5)/1#

Please observe that #a = 1, b = 2, and c = 1#; this gives us the parametric forms:

#x = t+ 3, y = 2t-2, and z = t+5#