How do you find the vector equation and parametric equations for the line through# (0, 14, -10)# and parallel to the line:#x = -1+2t, y = 6-3t, z = 3+9t#?

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Answer 1 · 2016-08-17T17:53:10

#{ (x = 2t), (y=14-3t), (z = -10+9t) :}#

The usual parametric representation is written as

#p=p_0+t vec v#.

Here we have

#p = {x,y,z}#
#p_0 = {-1,6,3}#
#t in RR#
#vec v = {2,-3,9}#

So, given

#p_1 = {0,14,-10}#

the parallel line is given by

#p = p_1 + t vec v#

which detailed is

#{ (x = 2t), (y=14-3t), (z = -10+9t) :}#