Distance from a point in space to a plane given a perpendicular line

[mill]

Homework Statement

Find the distance from the point A = (1; 0; 2) to the plane passing through the point (1; 2; 1) and perpendicular to the line given by the parametric equations x = 7, y = 1 + 2t, z = t - 3.

Homework Equations

d = | (PS dot n)/|n||

The Attempt at a Solution

Set n = <0, 2, 1> from the line given

|n|= sqrt(5)

I am confused about finding the S point. Would the second point be the one that passes through the plane?

If so,

PS = <0, -2, -1> so PS dot n = <0, -4, -1> and it would become something like -4/sqrt(5) + -1/sqrt(5). I get -5sqrt(5)/5 which becomes |-sqrt(5)|.

In general, when do we use intercepts (recommended by the textbook) and how vs just the point on the plane?

 

[LCKurtz]

Homework Statement

Find the distance from the point A = (1; 0; 2) to the plane passing through the point (1; 2; 1) and perpendicular to the line given by the parametric equations x = 7, y = 1 + 2t, z = t - 3.

Homework Equations

d = | (PS dot n)/|n||

The Attempt at a Solution

Set n = <0, 2, 1> from the line given

|n|= sqrt(5)

I am confused about finding the S point. Would the second point be the one that passes through the plane?

S is any point on the plane. Since you were given (1,2,1) just use it.

If so,

PS = <0, -2, -1>

Check your signs on PS.

so PS dot n = <0, -4, -1> and it would become something like -4/sqrt(5) + -1/sqrt(5). I get -5sqrt(5)/5 which becomes |-sqrt(5)|.

In general, when do we use intercepts (recommended by the textbook) and how vs just the point on the plane?

I guess it depends on what problem you are solving. Just fix your arithmetic and you should be OK here.