Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] P to AC

Given an ABCD.EFGH cube whose its side length is 8 cm. The point P is within AB so that AP = 3PH. The distance between P to AC is ....
A.

cm
B.

cm
C.

cm
D.

cm
E.

cm

So AH is

cm and PH =

. What do I do now? Is the triangle HPC a right triangle?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] P to AC

Again I'm having to assume that E is 'above' A etc.  I agree with your answer to AH but have no idea how you got PH.  Please explain.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] P to AC

Sorry, I meant P is within AH.

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] P to AC

Thanks.  This is an edited version of the post taking into account my new thinking on this problem. 

I've set up 3D coordinates as follows:

Origin A.
x axis AD
y axis AB
z axis AE.

As P is on AH with AP = 3.PH this means that P is 3/4 of the way along AH.

Using this, P has coordinates (6,0,6)

Let Q be on AC so that PQ is perpendicular to AQ (ie. PQ is the shortest distance between P and AC)

Let Q be (j,j,0) for some number j.

Using row vectors:

PQ = ( j-6, j-0, 0-6 ) and AQ = ( j, j, 0 )

If these are perpendicular to each other then their dot product is zero:

So Q is the point ( 3, 3, 0 )  So

Bob

Last edited by Bob (2018-04-09 11:16:32)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] P to AC

This is to 'bump' my previous post as I have edited it.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] P to AC

Okay, I get it. Thanks for your help.

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.