Allright, I've got mock-exams coming up this winter and I'm struggling with the damn vectors. I made a thread about this before but it turned out terrible due to my poor English skills and because I wrote it in a rush. Anyway:(adsbygoogle = window.adsbygoogle || []).push({});

The problem: Plane α: x-2y+z=2. Plane β: 2x+y+z=5

Point P= (0,1,4) is on the line of intersection, which has the directional vector L, between the two planes.

So L=directional vector of the line of intersection between the two planes.

A sphere is touching plane alpha at point A and plane beta at point B. Show that PB is perpendicular to L and the directional vector of plane Beta, and that PA is perpendicular to L and the directional vector of plane Alpha. Find the coordinates for the centre of the sphere, point S.

point A=(11,9,9) point B= (4,-14,-1).

My work: I found L by finding the cross product between the 2 directional vectors of the planes. I also confirmed that vectors PB & PA are both perpendicular to L, and PB is perpendicular to the directional vector of plane alpha while PA is perpendicular to the directional vector of plane beta.

Where I'm stuck: I set the centre coordinates as: x,y,z. Using some geometry I set up a parametric function where x= 7t y=21t+1 z=4.

I then figured that the radius of the sphere equals= (11-x)^2 + (9-y)^2 + (9-z)^2 = |SA| = |SB| = (-4-x)^2 + (14-y)^2 + (-1-z)^2. This is derived from the formula of a sphere.

Well, I tried to do the algebra, substituting x with 7t, y with 21t+1 and z with 4 but I just ended up with 0t=0.

I tried finding the radius as well, but these attempts too failed.

I spent almost 2 hours on this but I simply couldn't do it, it was (and still is) too hard for me. Can somebody here please help?

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# Homework Help: A sphere between two non-paralell planes - finding the centre

Can you offer guidance or do you also need help?

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