00:02
Hello, we are given a matrix with some of the entries undetermined.
00:07
We have to determine them or find them such that the matrix becomes a frame matrix or a matrix of a frame.
00:15
In a frame matrix, these entries make up a vector called the normal vector.
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These entries make up a vector called the orientation vector and these entries make up a vector called the approach vector.
00:30
And we have that these vectors n, o, a are unit vectors and n is equal to o cross a.
00:40
Now let us find out what is o cross a.
00:43
Let us find out, yeah, it is the determinant of ijk 0 0 minus 1 minus 1 0 0.
00:51
When we do that, we get i times 0 plus j times 1 plus k times 0.
00:56
So we get the vector 0 1 0 and this must be, well, we get the vector and this must be this vector so that the matrix with this place is filled in is 0 1 0 0 and the rest of the matrix.
01:26
And there is a unique way to complete this into a frame matrix.
01:30
In question number 2 .8, we are also given a matrix with some entries undetermined.
01:40
We have to complete the matrix so that this becomes a frame matrix.
01:44
Let us denote these two entries as a and b and this entry as c respectively so that the matrix, given matrix is this thing.
01:55
Now let us apply this condition n equal to o cross c.
01:59
So we have ijk c 0 minus 1 over root 2 0 1 0.
02:06
Its cross product is i times 1 over square root of 2 j times 0 plus k times c.
02:12
This must be equal to i times 1 over square root of 2 j times a plus k times b...