(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Im working currently with vectors. The question asks for the distance between two planes given by the two following equations:

x + y -2z = 0

3x + 3y -6z = 1

2. Relevant equations

I know the planes, H1, and H2 are parallel, so I can pick any random point on either, call the point Q, use the other plane as my H, and apply the following formula:

distance(H,Q) = (q-p) dot (n/|n|)

3. The attempt at a solution

Im assuming that someone familiar with vectors and lin. alg is going to answer this so Im not writing the whole essay. But yea if more explanation is needed then let me know.

For H I chose the first plane, so that n from plane 1 is (1, 1, -2). Correct me if Im wrong but I understand that you do need to pick the appropriate plane/line to use the right n? Or can it be either?

For Q on plane 2 I did - (1/3, 0, 0)

For a point P on plane 1 I chose (0,0,0)

After using the corresponding position vectors for the two points, I plug them in the formula and get the result:

(1)/(3√6), but my answers say it is (√6)/(9)

Thanks all.

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# Distances between planes (intro lin alg class)

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