00:01
Find a distance between the given point and the given line equations of our point has coordinates 2 1 minus 1 and our line is parametized as x equal to 2 t, y equal to 1 plus 2 t, and lastly z equal to 2 t.
00:34
Let's draw an illustration to help with our problem, so let's draw some line, and we want to find distance between the point, particularism between the point and our lines of this distance right here.
00:53
So as typical lines are defined by their directional vector v.
01:00
And if we choose some point on our line, say q, and we compute the vector pq, we can find the distance d by using our formula for our orthogonal projection.
01:26
So we find that distance d.
01:30
Is given by, or rather this vector here, i'll call this vector d.
01:54
This vector is given by v .pq divided by v.
02:11
Dot v.
02:11
In direction of vector v.
02:13
From here we can apply the magnitude.
02:18
So distance d will be given by the magnitude v...