00:01
Okay, so we have this vector v and we want to find two linearly independent vectors, which are perpendicular to the vector v.
00:07
So firstly, if we take the vector u1 to be the vector 1 -0 minus 1, then we get that u1.
00:16
Dot v is 1 times 1, which is 1 plus 5 times 0, which is 0, plus 1 times minus 1, which is minus 1.
00:29
So this is equal to zero.
00:31
So this vector is indeed perpendicular to v.
00:34
Now we need to find a different vector, u2, which is also perpendicular to v, which is linearly independent with this vector.
00:43
So what we're going to do is just make sure that we have some component in the second place or some non -zero number in the second component, and this is going to ensure that it ends up being linearly independent.
00:56
So if we take the first component to be zero, the second component to be 1 and the last component to be minus 5.
01:05
Let's see what we get if we do u2 .v...