- #1

Annabelle1234

- 4

- 0

## Homework Statement

The normal vector of each of the following planes is determined from the coefficients of the x-, y-, z- terms.

pi1: a1x+b1y + c1z + d1=0

pi2: a2x+b2y+c2z+d2=0

pi3: a3x+b3y+c3z+d3=0

Define the extended vector for each plan as follows:

e1= [a1, b1, c1, d1]

e2= [a2, b2, c2, d2]

e3=[a3, b3, c3, d3]

Use the extended (where necessary) and normal vectors of these planes to express the following geometric conditions:

a) 3 parallel, distinct planes

b) 2 parallel distinct planes intersected by another plane to form 2parallel lines

c) 3 distinct planes intersecting in a line

d) 3 distinct planes forming a triangular prism, that is, no common points of intersection but intersecting in pairs to form 3 parallel lines

e)3 distinct planes intersecting in a unique point

## The Attempt at a Solution

I am not really sure how to go about doing this. I tried simply trying to plug in numbers for the variable but i was unsuccessful. The examples in the textbook also doesn't help much. I would really appreciate it if someone could guide me onto how I could start this.

This is the first time I've posted a question here; I really hope you guys can help me solve this.

Thanks in advance! =)