9.6 The Distance From A Point to a Plane

Question 1

how to calculate the distance between a point and a plane?

Answer 1

1. Label the A,B C values
2. label the xo,y0,z0 values
3. use the distance between a point and a plane formula to calculate the distance

Question 2

what is the distance between a point and a plane formula?

Answer 2

d=|Axo+Byo+Czo+D|/square root A^2+B^2+C^2

Question 3

how to determine the distance between two planes?

Answer 3

1. find a point on the first plane
2. use the point, the other plane, and the distance between a point and a plane formula to calculate the distance

Question 4

how to find the equation of a plane midway between two planes?

Answer 4

simply add the two planes together

Question 5

how to determine the coordinates of the equidistant for the two planes

Answer 5

find coordinates that make the answer for the two planes added up true

Question 6

how do you make an equation of a plane given three points?

Answer 6

lets say the points as A,B and C

1. find the vector of AB
2. find the vector of AC
3. take the cross product of the two vectors and label the answer (a,b,c)
4. use the equation a (x-xo)+b(y-yo)+c(z-zo)

Question 7

how do you determine the value of A given a point, a cartesian equation and the distance?

Answer 7

1. write the distance between a point and a plane formula
2. plug in the values you know
3. isolate for A

Question 8

how to do you determine the distance between two planes?

Answer 8

1. write the direction vectors of both the planes, label them m1 and m2
2. take the cross product of the two direction vectors, label the answer (A,B,C)
3. use the direction vector and a point from the first vector equations to isolate for D, and form a cartesian equation
4. use the cartesian equation, the point from the second vector equation and the distance between a point and a plane formula to find the distance