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.

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.