Determine two sets of parametric equations for the line passing through the points P(1,7,1) and Q(3,4,4)

Question

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:???

Answer 1

why not use the other point?

x = 3 - 2x
y = 4 + 3s
z = 4 - 3s

Answer 2

I was thinking about that, ha~ but thought it would be wrong.

Thanks!

Answer 3

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.