Problems from Parametric equations of a straight line in the space

Consider the points $A = (2, 1, - 2)$ and $B = (1, - 2, 3)$ , and find the parametric equations of the straight line that goes through $A$ anb $B$ .

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Development:

We will start computing a director vector of the straight line: $\vec{A B} = B - A = (1, - 2, 3) - (2, 1, - 2) = (- 1, - 3, 5)$

Therefore, with the director vector and point $A$ , we obtain the parametric equations: ${\begin{cases} x = 2 - k \\ y = 1 - 3 k \\ z = - 2 + 5 k \end{cases}$

Solution:

${\begin{cases} x = 2 - k \\ y = 1 - 3 k \\ z = - 2 + 5 k \end{cases}$

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