00:01
All right, now we've got a three -dimensional line.
00:07
So it's written in parametric form.
00:13
X as a function of t is 2t negative 4 minus t 3t.
00:28
And we want the distance from that to the point p, which is 4, 1 .1.
00:36
1, negative 1.
00:39
So first, i want to find a point q that is on the line.
00:47
I'm going to let t equals 0.
00:51
And so that's going to be the point 0, negative 4 minus 0, which is negative 4, and 3 times 0 is 0.
01:02
So that point is on the line.
01:06
Now, a vector that is in the direction of the line, if we let, if we just take the numbers that come before t, the coefficients of t in our parametric point, they are 2, negative 1, and 3.
01:37
So that would be a vector.
01:39
And lastly, we need the vector w that extends from point q to point p.
01:54
So it's just going to be p minus q.
01:57
So that's going to be 4 minus 0 is 4.
02:00
1 minus negative 4 is 5.
02:04
Negative 1 minus 0 is negative 1.
02:10
So the component of vector w in the direction of vector v is going to be this expression, this expression, which i always like to write as this, because it shows me exactly what i'm doing...