Line through 2 Points

Line through 2 Points:

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Find the parametric and symmetric equations of the line through

P₁(-3, 2, -5) and P₂(2, -1, -3).

We need to find a vector parallel to the line by using the vector between the two points:

a = P₁P₂ = i[2 - (-3)] + j[-1 - 2] + k[-3 - (-5)] = 5i - 3j + 2k.

Now use the components of a to express the equation of the line (using P₁):

Parametric:

x = -3 + 5t; y = 2 - 3t; z = -5 + 2t

Symmetric: (Solve for t in each of the above)