Answer:
The equation is:
(1/a)x + (1/b)y + (1/c)z = 1
Step-by-step explanation:
The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:
<0 - a, b - 0, 0 - 0>
<-a, b, 0> .....................(1)
The direction vector between (0, 0, c) and (0, b, 0) is given as:
<0 - 0, b - 0, 0 - c>
= <0, b, -c> .....................(2)
To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).
Doing this, we have:
<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>
To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:
(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0
(bc)x + (ac)y + (ab)z = (ac)b
Dividing both sides by abc, we have:
(1/a)x + (1/b)y + (1/c)z = 1
