basic linear algebra questions

let ABC be a triangle and let p be the midpoint of side AB

let http://i52.photobucket.com/albums/g37/mmmmms/1-7.jpg and http://i52.photobucket.com/albums/g37/mmmmms/2-6.jpg

express http://i52.photobucket.com/albums/g37/mmmmms/5-3.jpg and http://i52.photobucket.com/albums/g37/mmmmms/6-2.jpg in terms of http://i52.photobucket.com/albums/g37/mmmmms/7-1.jpg and http://i52.photobucket.com/albums/g37/mmmmms/8-1.jpg and http://i52.photobucket.com/albums/g37/mmmmms/9-1.jpg

hence prove that the midpoint of the hypotenuse of a right-angle triangle is equidistant from the three vertices

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let p be the plane with cartesian equation 2x+y-3z=9 and let A,B be points with coordinates (1,-2,3) and (-2,1,-1)

l is the line passing through the point A and B

find the coordinates of the point C where the line l intersects the plane p

i have no ideas how to find the intersection between a line and a plane

thx