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**[SOLVED] A plane and a point and another point**

**1. Homework Statement**

According to the Flat Earth CLub, Earth is a plane described by the equation

x+y+z = 18

Also according to the Flat Earth Club, Earth will be destroyed on the day this assignment is due by an explosion that will spontaneously occur at the so-called "armageddon point" A = (1,1,1). It so happens that the school (considered as a point) will be the first place on Earth that is destroyed by this explosion (how sad)

**2. Homework Equations**

a) Calculate the coordinates of the school.

b)What is the distance between A and the school. What is the distance between A and Earth?

**3. The Attempt at a Solution**

a. Form the line that passes through point A with a direction vector that is parallel to the normal vector of the plane.

L: (x,y,z) = (i + j + k) + (i + j + k)t

= (1 + t)i + (1+t)j + (1+t)k

Now substitute into the equation of the plane to determine the point of intersection P.

x = t + 1

y = t +1

z = t + 1

(t+1) + (t+1) + (t +1 ) = 18

3t + 3 = 18

3t = 15

t = 5

The point P is then (6, 6, 6)

b. The distance (D) between A and the Earth/Monash Universtiy (P) which are 3-D points, is calculated by:

D = √[(px-ax)2 + (py-ay)2 + (pz-az)2]

Where P = (px, py, pz) and A = (ax, ay, az)

Therefore: P = (6,7,8) and A = (1,1,1) and

D= √[(6-1)2 + (6-1)2 + (6-1)2

= √75

= 8.66