Determine two sets of parametric equations for the line passing through the points P(1,7,1) and Q(3,4,4)
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I got one of them but I don't know how to get a second parametric equation.
first one: x=1-2s, y=7+3s, z=1-3s
second:???
why not use the other point?
x = 3 - 2x
y = 4 + 3s
z = 4 - 3s
I was thinking about that, ha~ but thought it would be wrong.
Thanks!
To find a second set of parametric equations for the line passing through the points P(1,7,1) and Q(3,4,4), we can use the parameter t instead of s.
First, let's calculate the direction vector of the line, which is the vector PQ. We get:
PQ = Q - P = (3,4,4) - (1,7,1) = (2,-3,3)
Now, we can find the second set of parametric equations by adding the direction vector to the initial point P.
Second set: x = 1 + 2t, y = 7 - 3t, z = 1 + 3t
In these equations, t can take any real value. By substituting different values of t, you can generate different points on the line passing through P and Q.