Question

find an equation of the plane with x-intercept (a,0,0), y-intercept (0,b,0), z-intercept (0,0,c) where a,b,c are positive real numbers.

Answer 1

Im not sure where to start

Answer 2

equation of a plane is Ax+By+Cz+D=0

Answer 3

u have three points that satisfies this equation
(x,y,z)=(a,0,0),(0,b,0),(0,0,c)

Answer 4

for example
A*a+B*0+C*0+D=0 then A=-D/a

Answer 5

try to find B and C

Answer 6

so B = -D/b ?

Answer 7

yes

Answer 8

(-D/a)x + -D/b(y) + (-D/c)z = 0

Answer 9

emmm
(-D/a)x + -D/b(y) + (-D/c)z+D=0

Answer 10

now eliminate D

Answer 11

how?

Answer 12

you have
\[\frac{x}{a}D+\frac{y}{b}D+\frac{z}{c}D-D=0\]

Answer 13

divide it by D

Answer 14

what is result?

Answer 15

z/a + y/b + z/c = 1

Answer 16

almost done

Answer 17

isnt that the answer? I was not given values for a,b, or c

Answer 18

thats the answer
a b and c are fixed constants

Answer 19

thank you!

Answer 20

yw