Find parametric equations and symmetric equations for the line. The line thr

FizeauV

FizeauV

Answered question

2021-10-20

Find parametric equations and symmetric equations for the line.
The line through the origin and the point (4, 3, -1)

Answer & Explanation

unessodopunsep

unessodopunsep

Skilled2021-10-21Added 105 answers

The direction vector for a line through the origin (0,0,0) and the point (4,3,-1) is
4,3,1
Which you can confirm by subtracting one point from the other.
Plug the direction vector into a,b,c and pick one of the points (the origin is easier) into x0,y0,z0
x=x0+at,y=y0+by,z=z0+ct
x=0+4t, y=0+3t, z=0+(1)t
x=4t, y=3t, z=t
For the symmetric equations, solve each of the parametric equations for t and set equal to each other.
t=x4   t=y3,   t=z
x4=y3=z
Results:
parametric: x=4t,y=3t z=t   symmetric:x4=y3=z

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