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.

sorry not sure

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet