Problems from Vector equation of a straight line in the space

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

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

Therefore the vector equation is: $(x, y, z) = A + k \cdot \vec{A B} = (2, 1, - 2) + k \cdot (- 1, - 3, 5)$

$(x, y, z) = A + k \cdot \vec{A B} = (2, 1, - 2) + k \cdot (- 1, - 3, 5)$

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