Steve Herr is an architect in Minneapolis, Minnesota. His latest project is designing a park. On the blueprint, the park is determined by a plane which contains the points at (1,0,3), (2,5,0), and (3,1,4) One of the features of the park is a monument that must be perpendicular to the ground. Find a nonzero vector, representing the monument, perpendicular to the plane defined by the given points.

8i - 7j - 9k

Step-by-step explanation:

We have three points:

A (1,0,3)

B (2,5,0)

C (3,1,4)

First of all, we write the following two vectors:

These two vectors connect A with B and B with C, and since these 3 points lie on the plane, the two vectors also lie on the plane.

Therefore, the cross product of these two vectors must be a vector perpendicular to the plane.

The cross product of the two vectors is:

And the equation of the plane can be found as:

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

25% is the answer