FIRST PRACTICE MIDTERMThe following five questions are worth 20 points each, although many havemultiple parts. Show ALL your work in your answers to each question. Youhave 75 minutes for the examination. Calculators are NOT permitted.1.LetP, Q,andRbe points inR3with coordinatesP= (0,2,1),Q=(2,0,1),R= (0,0,-1).1a. Give a parametrization (in terms of auxiliary variablestandu) for theplane containingP,Q, andR.1b. Give an equation of the formax+by+cz=dfor the plane containingP,Q, andR.2.Draw the level setsf(x, y) =cfor the given values ofc, in the givendomains.2a.f(x, y) =|x|+|y|,-2≤x≤2,-2≤y≤2,c=-1,0,1,2,3,4.2b.f(x, y) =xy,-2≤x≤2,-2≤y≤2,c=-2,-1,0,1,2.3. Define vectors~u,~vinR3by~u= (-2,1,0),~v= (0,2,-1). Letθbe theangle between the two vectors.3a. Compute the lengths of~uand~v.3b. Compute cosθ.3c. Give a unit vector orthogonal to both
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