Question

What changes would you make in your description of point, line, and plane?

Answer 1

Answer:

Here's a quick sketch of how to calculate the distance from a point P=(x1,y1,z1)

P

=

(

x

1

,

y

1

,

z

1

)

to a plane determined by normal vector N=(A,B,C)

N

=

(

A

,

B

,

C

)

and point Q=(x0,y0,z0)

Q

=

(

x

0

,

y

0

,

z

0

)

. The equation for the plane determined by N

N

and Q

Q

is A(x−x0)+B(y−y0)+C(z−z0)=0

A

(

x

−

x

0

)

+

B

(

y

−

y

0

)

+

C

(

z

−

z

0

)

=

0

, which we could write as Ax+By+Cz+D=0

A

x

+

B

y

+

C

z

+

D

=

0

, where D=−Ax0−By0−Cz0

D

=

−

A

x

0

−

B

y

0

−

C

z

0

.

This applet demonstrates the setup of the problem and the method we will use to derive a formula for the distance from the plane to the point P

P

.

Step-by-step explanation: