9.5 Distance from a point to a line in R^2 and R^3

Question 1

how to calculate the distance between parallel lines in vector equation form?

Answer 1

1. write the point from one of the planes and call it A
2. write the parametric equations of the other plane
3. make the parametric equation into a point and call it C

4.find the direction vector of AC

5. calculate the dot product of AC and the direction vector and solve for t
6. determine point C by plugging in the t value
7. calculate the distance between point A and C

Question 2

how to calculate the distance between two lines in vector equation form

Answer 2

1. write the parametric equations of the other plane
2. write the point from one of the planes and call it A
3. make the parametric equation into a point and call it C

4.find the direction vector of AC

5. calculate the dot product of AC and the direction vector and solve for t
6. determine point C by plugging in the t value
7. calculate the distance between point A and C

Question 3

what is the distance between two points formula?

Answer 3

d=square root (x2-x1)^2+(y2-y1)^2+(z2-z1)^

Question 4

how to calculate the distance between two parallel planes?

Answer 4

1. find a point in one of the planes

2.Use the point, the other plane and the distance between a point and a plane equation to find the distance

Question 5

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

Answer 5

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

Question 6

How to calculate the distance between a point and line in vector equation form?

Answer 6

1. Label the point given as point P
2. Label the point in the vector equation as point Q
3. Find the direction vector of PQ
4. Label the direction vector in the vector equation as M
5. Find the cross product of direction M and PQ
6. Use the formula of the distance between a point and a line to find the distance

Question 7

How to determine the coordinates of a point on the line in vector equation form that produces the shortest distance between the line and a point?

Answer 7

1. Label the point given A
2. Write the parametric equations of the vector equation
3. make the parametric equation into a point and call it C
4. find the direction vector of AC
5. calculate the dot product of AC and the direction vector and solve for t
6. determine point C by plugging in the t value. the C point is the answer

Question 8

what is the distance between a point and a line equation?

Answer 8

d=|m X QP|/|m|

Question 9

how to calculate the distance between two parallel lines in vector equation form?

Answer 9

same steps as finding the distance between two lines vector equation form

1. write the point from one of the planes and call it A
2. write the parametric equations of the other plane
3. make the parametric equation into a point and call it C
   4.find the direction vector of AC
4. calculate the dot product of AC and the direction vector and solve for t
5. determine point C by plugging in the t value
6. calculate the distance between point A and C