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◦. u = (-8,-4,6,3) , v = (5,3,6,4)

The Euclidean distance between these two vectors is .

The angle is obtuse.

Step-by-step explanation:

Suppose we have two vectors, u and v, in which:

The Euclidean distance between these two vectors can be given by the following formula:

To find the cosine of the angle between two vectors u and v, we use the following formula:

In which is the dot product between vectors u and v, is the norm of vector u and   is the norm of vector v.

If is negative, the angle is obtuse. If it is 0, the angle is 90º. And if it is positive, the angle is acute.

In this problem, we have that:

The Euclidean distance:

Cosine of the angle

Since the cosine is negative, the angle is obtuse.

what are the statements

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq