1. The problem statement, all variables and given/known data Question 1. Given position vectors OA : i+2j-k and OB: 2i+j+3k in a 3D Cartesian space with origin O of the points A and B. a) Find the scalar equation of the plane which contains A and which is perpendicular to vector AB. b) Find the shortest distance from the point (1,-1,1) to the plane obtained in a (a) 2. Relevant equations 3. The attempt at a solution Here is what i did (a) Equation of line AB r= (2,1,3)+ t(1,-1,4) AP.n = 0 OP.n = OA.n (x,y,z).(1,-1,4) = (2,1,3).(1,-1,4) x-y+4z = 13 [equation of plane]? (b) vector form of plane => r.(1,-1,4) = 13 line equation => r= (1,-1,1) + t(1,-1,4) Using r=r for both equations i get t= 2/9 Substitute t=2/9 into line equation giving me (11/9, -2/9, 17/9) I'm stuck here then for part (b) I'm pretty weak in this chapter, couldn't seem to grab the concept here. 1. The problem statement, all variables and given/known data Question 2. Obtain the scalar equation of the plane which passes through point P(1,2,3) and contain a straight line x(t)= 3t y(t)= 1+t z(t)= 2-t t is the parameter of the line 2. Relevant equations 3. The attempt at a solution Equation of the line= (0,1,2) + t(3,1,-1) Let Q and R be the points on the line t=0 Q=(0,1,2) t=1 R= (3,2,1) Therefore PQ= (-1,-1,-1) PR= (2,0,2) PQxPR= (-2,0,-2) Thus the equation of the plane a(x-x1) + b(y-y1) + c(z-z1)= 0 -2(x-1) + 0 -2(z-3) = 0 -2x - 2z + 8 = 0 is this correct?