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13 The planes p, , p, and p, have equations x=1 , 2x+ y + az =5 and x + 2y+ z=b respectively where a and b are real constants. Given that p, and p, intersect in a line l, show that a vector equation of l, is r =i+ (3-la)j+ 2k , where 1 is a real constant. (a) Given that the acute angle between / and p, is 60, find the possible values of a. L (b) Given that the shortest distance from origin to p, is - , determine the possible position vectors of the foot of perpendicular from the origin to P3 . [2012/NJC/Prelim/1/6 modified]