00:02
So if a line, let's call it l, is perpendicular to the vector, we'll call a, equal negative 5 comma 4, then l has the equation, the equation, negative 5x plus 4y equals, i'll say d, for some real number d.
00:43
So where does this come from? well, i mean, it should be clear to see the negative 5 comes down here, and then the 4 comes down.
00:58
And so the idea is basically that, you know, if you take a point x comma y on the plane and then take its dot product with this vector a, you should get zero.
01:20
Or sorry, the dot product shouldn't be zero between a point and a, but the dot product of the direction of the line l and the vector a should be zero, because that's what it means for these two vectors to be perpendicular.
01:35
Now we want our line, so this is our line, but we don't know what d is, but now we want it to contain the point 3 comma 2, then we can solve for d...