Find the Euclidean distance between u and v and the cosine of the angle between those vectors. State whether that angle is acute, obtuse, or 90^(circ). u = (-1, -1, 8, 0), v = (5,6,1,4)

Vectors and spaces
asked 2020-10-21
Find the Euclidean distance between u and v and the cosine of the angle between those vectors. State whether that angle is acute, obtuse, or \(\displaystyle{90}^{{\circ}}\). u = (-1, -1, 8, 0), v = (5,6,1,4)

Answers (1)

The Eunclidean distance between u and v is the Euclidean norm of the vector u - v. Thus, we must find
Furthermore, the angle 0 between these vectors is given by
where \(\displaystyle{\left\langle{u},{v}\right\rangle}\) is a scalar product of u and v. So we compute
which means that
So, this angle is obtuse.
It is obtuse.

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