Distance between vector and a plane proof

[TyroneTheDino]

Homework Statement

Homework Equations

Since this a proof. Most of the equations I needed were involved in the solution I created.

The Attempt at a Solution

I believe my proving is valid; however, I was wondering if I might have missed a step or did some math that didn't make sense,

 

[Mark44]

Homework Statement

Homework Equations

Since this a proof. Most of the equations I needed were involved in the solution I created.

The Attempt at a Solution

I believe my proving is valid; however, I was wondering if I might have missed a step or did some math that didn't make sense,

Your proof is going in the right direction, but your handwritten work is hard to read in places (especially the latter half), is not well organized, and your notiation is sloppy in several places.

We prefer that posters show the work, either as plain text or using LaTeX, instead of posting images. Images are often difficult to read, and we can't insert a comment into the middle of an image to point out an error.

We have a LaTeX tutorial here -- https://www.physicsforums.com/help/latexhelp/
Most of what you have written in longhand can be done fairly simply in LaTeX:

• Vectors -- $\vec{PQ}$ -- the script for this is # #\vec{PQ}# # (no spaces between the # characters
• Fractions -- $\frac{u + v}{w}$ -- this is # #\frac{u + v}{w}# #
• Dot product - use \cdot to make that dot
• Cross product - use \times

The only place where an image would be helpful is your sketch of the plane and the points in it and point Q.

Some of the places where your notation is sloppy are in your last equation, which looks like this:
$$\frac{\vec{PR} \cdot (\vec{PS} \times PQ)}{|\vec{PR} \times P} = \frac{PQ \cdot (\vec{PR} \times \vec{PS})}{DR \times PS}$$
I have written the above exactly as it appears in the image you posted.
The main things wrong are the following:

• You are missing a | in the denominator on the left side of the equation.
• You wrote P in the denom. on the left side - you probably mean PS.
• On the right side, you are missing the absolute values in the numerator.
• On the right side, in the denominator, what you wrote looks like DR, not PR.
• Also in the right side denominator, PR X PS is a vector, and division by vectors is not defined. You need the magnitude bars there for the norm of that vector.

Nits
Try to be consistent in writing the arrows above your vectors. Some of them you put in, and some you don't. Either put them everywhere they belong or don't put them anywhere.

 

[TyroneTheDino]

Thank you for the feedback. I will make sure to use latex ask questions about future problems!