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# Hey y'all,

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Hey y'all,

So, I am incredibly confused on this question, and I am none the wiser on how to solve it,

A cube whose side length is 5 is shown below. Let P be on edge AB such that AP = 2, and let Q be on edge AE such that AQ = 1. The plane passing through points C, P, and Q intersects DH at R. Find the length DR.

Oh, and if possible, please explain what you did step by step, that would greatly appreciated! Jan 16, 2023

#1
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Could you give us a lift into what maths your expected to use ?

There are several methods that could be used.

What are you currently working on ?

Vectors, 3D co-ordinate geometry, what ?

Jan 16, 2023
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Currently, I'm working on 3D Prisms. Oh, and, I'm sorry I took so long to respond to you, I didn't check this post until just now. Qube73  Jan 16, 2023
edited by Qube73  Jan 16, 2023
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To find the length of DR, we can use the Pythagorean theorem. We know that the length of AC is 5 and the length of AQ is 1. Using the Pythagorean theorem, we can find that the length of CQ is 4. Now we know that CR is a right triangle, we can use the Pythagorean theorem again. We know that the length of CQ is 4 and the length of DR is unknown. Applying the Pythagorean theorem, DR = sqrt(5^2-4^2) = sqrt(9) = 3. so, DR = 3.

Jan 17, 2023
#5
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Still don't know what method you're expected to use, so I'll just take you through the easiest, (leaving you to fill in the detail).

To begin with though ignore answers #2 and #4, both are incorrect.

#2 is from one of the sites dimwits and #4 is just simply incorrect, beginning with AC = 5, and then ignoring the point P, which is needed to determine the plane CPQ.

Basically, the method is 3D co-ordinate geometry, find the equation of the plane passing through C P and Q, substitute the two known co-ordinates of R, and out pops the third.

So, let A be the origin of the co-ordinate system with AD as the x-axis, AB the y-axis and AE the z-axis. You should then be able to write down the co-ordinates of the points P Q and C. (P will be (0, 2, 0) for example).

The equation of a plane in 3D can be written as ax + by + cz = 1. Substitute the co-ordinates of  P Q and C to determine the values of a b and c and then, having done that, substitute the two known co-ordinates of R. The third co-ordinate of R (the one that you need), drops out.