Finding the Height and line equation of a plain

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  1. Create the equation of the median and the height From A where ABC is a triangle, find the angle between median and the height from A.

$$A(2, 0); B(1, -2), C(3, 6)$$

Solution:

If M is the middle point between A and C it has cordinates M(2, 2). The equation of the median can be found with:

$$(x-M1)/(M1-A1) = (y-M2)/(M2-A2)$$ $$0y=2x-4$$

How can I get the height AH ?
  1. Create the equation of the sides of a triangle ABC if it's given B(1, -2) and the height h: x + 4y -2 =0 and the median *m : x = 2 *. h is the height which comes from B, m is median which comes from B:

Solution:

How do we solve this one ?
  1. Create the equation of the plain a, containing the points A(4, -1, 0); B(2, 1, 2); * C(6, 3, 2) * and the line l which goes through the points M(2, -3, 4) and N(3, -5, 7).

Solution:

How do we solve this one ?
  1. make a equation of the plain a containing

$$l1: x = λ +3; y = −λ; z = λ$$ $$l2 : x = µ +1; y = −µ; z = µ +4$$

and find the projection of the line $$l:x = 2t+1; y = t +1 ; z = 3t+1$$ on a

Solution:

How do we solve this one ?

PS. Sorry for the bad MathJax and the dumb question