Find an equation of the plane with the given characteristics. The plane passes through the points (4, 3, 1) and (4, 1, -7) and is perpendicular to the plane 8x 7y 4z

Step-by-step explanation:

Given

Perpendicular to

Required

Determine the plane equation

The general equation of a plane is:

For

First, we need to determine parallel vector

is parallel to the required plane

From the question, the required plane is perpendicular to

Next, we determine vector

This implies that the required plane is parallel to

Hence: and are parallel.

So, we can calculate the cross product

The product is always of the form + - +

So:

Calculate the product

So, the resulting vector, n is:

Recall that:

By comparison:

Substitute these values in

Recall that:

So, we have:

Collect Like Terms

Divide through by -16

Hence, the equation of the plane is

if x decreases by 4 then y increases by 10

step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.