Two planes, m and n, have equations x + 2y − 2ß = 1 and 2x − 2y + ß = 7 respectively.?
The line l has
equation r = i + j − k + λ(2i + j + 2k).
(i) Show that l is parallel to m.
(ii) Find the position vector of the point of intersection of l and n.
(iii) A point P lying on l is such that its perpendicular distances from m and n are equal. Find the
position vectors of the two possible positions for P and calculate the distance between them.
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i) ..compute the dot product of the plane vector with that of the line vector
ii)line has x = 1 + 2Γ , y = 1 + Γ , z = -1 + 2 Γ , put these into the 'n plane ' ,
solve for Γ; then x , y , z
iii) pick points P1 and P2 on the 2 planes , a point C(x,y,z) on the line..
compute the projection of CP1 onto m plane vector ; compute projection of CP2 onto n plane vector;
set these equal..solve for x , y , z...(use the x,y,z of ii)