How can I check the position of the lines in the pyramid?

KyleJ318ByKyleJ318

Good evening,

I have encountered a problem and am very unsure whether my calculation is correct:

A point S lying on the line h is the vertex of a right pyramid with the parallelogram ABCD as its base. The points P and Q are the midpoints of the sides BC and DS. Investigate the position of the lines AQ and SP.

Given are the points: A (5|-3|0), B (7|1|5), C (-2|0|1), D (-4|-4|-4) and S(-2.16|-13.83|11.83) as well as the intersection point of the diagonals M(1.5|-1.5|0.5).

Point P lies on side BC and Q on DS. I arrived at these vectors:

For example, for P on BC: (-9|-1|-4)/2 = (-4.5|-0.5|-2) Is this the coordinate of P? The position of line SP would then be (-2.34|13.33|-13.83)

How should I investigate this situation?

Thank you in advance!

(2 votes)
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LUKEars
LUKEars
9 months ago

So… Geogrid I come to the following sketch (see below)…

It is clear that the straight line AQ runs in the side surface ASD… and the straight line SP runs in the side surface BCS…

this is probably meant by “latitude of the straight lines”… so none of the straight lines passes through the pyramid…

and P=B+(C-B)/2=(C+B)/2=(-2|0|1) + (7|1|5))/2=(5|1|6)/2=(2,5|0.5|3)

or?

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