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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,263

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.

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?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.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

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

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

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,263

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.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

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 bundy (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

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,386

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

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,263

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.

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