00:01
We're going to find the projection v onto w.
00:05
I'm going to write these as vectors.
00:07
So v is negative 2, 8, and w is 1, negative 1.
00:16
The projection of v onto w is computed as the dot product of v with w divided by the length of w squared multiplied in the direction of w.
00:35
The dot product is just the product of the corresponding entries and then add it all up.
00:41
So 2 times negative 1 is negative 2 plus 8 times negative 1 is negative 8.
00:46
The length is just the sum of squares of the entries.
00:48
So that will be 1 plus 1 in the direction 1, negative 1.
00:53
This is negative 10 over 2.
00:55
So that's going to be negative 5 in the direction 1, negative 1.
01:00
Multiplying that out, we get negative 5, 5.
01:04
Okay, so the projection in terms of i and j is negative 5i plus 5j.
01:12
Okay, the second part, we want to decompose v into two vectors, v1 and v2...