# Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8).

Question
Vectors and spaces
Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8).

2020-10-19
Start at (5,−2,3)(5,−2,3) then to get to Q, you must travel in the direction of Q which is given by Q−P=(2,−7,8)−(5,−2,3)=(−3,−5,5). Now, traveling this direction in any scaled value gives you a line determined by the following vector equation:
$$(5,−2,3)+t(−3,−5,5) which you can write in parametric form: \(x=5−3t, y=−2−3t, and z=3+5t notice that all we did was just write it in a form that represents a formula for each point (x,y,z)(x,y,z). ### Relevant Questions asked 2020-11-16 Find the vector and parametric equations for the line through the point P=(5,−2,3) and the point Q=(2,−7,8). asked 2021-03-12 Let the vector space \(P^{2}$$
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