I have 3 dots of a triangle : a = (2,5), b = (6,-3), c = (-2,2) What are the equations of the Altitudes . In other words how do I find the perpendicular vector?
ac = [2--2,5-2]=[4,3]; so the perpendicular vector to ac is [-3,4] and the equation line (theAltitude from b to ac ) is : x = 6 -3t y = -3 +4t
is that correct?
First you want to find the general form of a point $d$ that lies on the altitude. Because the vector from $b$ to $d$ is perpendicular to the vector from $a$ to $c$, you can state:
$\vec{bd} \cdot \vec{ac} = 0$
Letting $d = x\mathrm i + y\mathrm j$, you get:$-4(x-6) - 3(y+3) = 0$
Set $x = 0$ to find one such point $d = (0,5)$.
In this case, $\vec {bd} = -6\mathrm i + 8 \mathrm j$, giving the equation:
$$\vec r = 6\mathrm i - 3\mathrm j + \lambda (-6\mathrm i + 8 \mathrm j)$$
which can also be parametrised $x = 6 -6\lambda, y = -3 + 8\lambda$.