How do I find an equation of the line that passes through the points #(2, -1, 3)# and #(1, 4, -3)#?

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Answer 1 · 2014-10-19T21:26:07

Let

#(x_0,y_0,z_0)=(2,-1,3)#,

and let the direction vector

#(a,b,c)=(1,4,-3)-(2,-1,3)=(-1,5,-6)#.

Since the parametric equations of the line can be written as

#{x-x_0}/{a}={y-y_0}/{b}={x-z_0}/c#,

we have

#{x-2}/{-1}={y+1}/{5}={x-3}/{-6}#.

I hope that this was helpful.