# C fall 2008 find the point q in the plane 2 x y 2 z

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Problem 2(c) - Fall 2008Find the pointQin the plane 2x+y-2z= 19 which is closest to thepoint (1,6,-1). (Hint: You can use part b) of this problem to help findQor first find the equation of the lineLpassing throughQand the point(1,6,-1) and then solve forQ.)
Problem 2(c) - Fall 2008Find the pointQin the plane 2x+y-2z= 19 which is closest to thepoint (1,6,-1). (Hint: You can use part b) of this problem to help findQor first find the equation of the lineLpassing throughQand the point(1,6,-1) and then solve forQ.)
Problem 3(a) - Fall 2008Find the volumeVof theparallelepipedsuch that the following fourpointsA= (3,4,0),B= (3,1,-2),C= (4,5,-3),D= (1,0,-1) arevertices and the verticesB,C,Dare all adjacent to the vertexA.
Problem 3(a) - Fall 2008Find the volumeVof theparallelepipedsuch that the following fourpointsA= (3,4,0),B= (3,1,-2),C= (4,5,-3),D= (1,0,-1) arevertices and the verticesB,C,Dare all adjacent to the vertexA.
Problem 3(b) - Fall 2008Find thecenterandradiusof the spherex2-4x+y2+ 4y+z2= 8.
Problem 3(b) - Fall 2008Find thecenterandradiusof the spherex2-4x+y2+ 4y+z2= 8.
Problem 5(a) - Fall 2008Consider the pointsA(2,1,0),B(3,0,2) andC(0,2,1). Find the area ofthe triangleABC. (Hint: If you know how to find the area of aparallelogram spanned by 2 vectors, then you should be able to solve thisproblem.)
Problem 5(a) - Fall 2008Consider the pointsA(2,1,0),B(3,0,2) andC(0,2,1). Find the area ofthe triangleABC. (Hint: If you know how to find the area of aparallelogram spanned by 2 vectors, then you should be able to solve thisproblem.)
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Problem 5(b) - Fall 2008Three of the four vertices of a parallelogram areP(0,-1,1),Q(0,1,0)andR(2,1,1).Two of the sides arePQandPR.Find the coordinates ofthe fourth vertex.