00:03
We have a line in parametric form, which, okay, i was thinking it wasn't three -dimensional.
00:17
4 plus 3 -t, but it is 3 -dimensional, 6 -2 -t.
00:26
And then we have a point 9 -0.
00:36
We want to find the distance from the line to the point.
00:40
Well, first of all, a point that is on the line.
00:43
Which i'm going to call q.
00:45
I'm just going to set t equal to zero, and that will be the point 460.
00:58
460, because when t is zero, that's what you get.
01:02
A vector that is in the direction of the line, which i'm going to call vector v, just like the book does, is going to be, we just look at.
01:17
At the coefficients on t, that's 3, 0, negative 1.
01:25
3t, 0 ,0, negative 1t.
01:30
And finally, a vector w, which extends from point q to point p, 9 minus 4 is 5, 0 minus 6 is negative 6, and 0 minus 0 is 0.
01:52
Now we can just use our equations.
01:58
So the projection of vector w onto vector v.
02:05
So this is the component of vector w in the direction of vector v is the inner product of w and v over the norm of v squared times vector v, which is going to going to be the inner product of w and v over the inner product of v and v times v.
02:46
Interproduct of w and v is going to be 15 plus 0 plus 0, just 15.
02:55
Interproduct of v and v is going to be 9.
03:00
3 squared is 9, negative 1 squared is 1.
03:04
That's it...