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Problem 1. Let u→=-1,-2,4{“version”:”1.1″,”math”:”u→=…

Problem 1. Let u→=-1,-2,4{“version”:”1.1″,”math”:”u→=-1,-2,4″} and v→=-5,6,-7{“version”:”1.1″,”math”:”v→=-5,6,-7″} be vectors. Part (a) (5 points) Find 2u→-v→{“version”:”1.1″,”math”:”2u→-v→”} Part (b) (5 points) Find u→{“version”:”1.1″,”math”:”u→”}, the magnitude of u→{“version”:”1.1″,”math”:”u→”} Part (c) (5 points) Find the unit vector in the direction of u→{“version”:”1.1″,”math”:”u→”} Problem 2. Let u→=2,2,-1{“version”:”1.1″,”math”:”u→=2,2,-1″} and v→=1,2,2{“version”:”1.1″,”math”:”v→=1,2,2″} be vectors. Part (a) (5 points) Find the dot product u→·v→{“version”:”1.1″,”math”:”u→·v→”} Part (b) (5 points) Find the cross product u→×v→{“version”:”1.1″,”math”:”u→×v→”} Part (c) (5 points) Find the angle between the two vectors u→{“version”:”1.1″,”math”:”u→”} and v→{“version”:”1.1″,”math”:”v→”} Problem 3. (15 points) Find an equation of the line L{“version”:”1.1″,”math”:”L”} passing through the points P(1,1,2){“version”:”1.1″,”math”:”P(1,1,2)”} and Q(1,-1,3){“version”:”1.1″,”math”:”Q(1,-1,3)”}, and then find the distance between the point R(0,0,5){“version”:”1.1″,”math”:”R(0,0,5)”} and the line L{“version”:”1.1″,”math”:”L”}. Problem 4. (15 points) Find an equation of the plane passing through the points P(1,-1,0){“version”:”1.1″,”math”:”P(1,-1,0)”}, Q(2,2,1){“version”:”1.1″,”math”:”Q(2,2,1)”}, and R(-1,-2,-1){“version”:”1.1″,”math”:”R(-1,-2,-1)”}. Problem 5. Consider the vector-value function r→(t)=t2,et,sint{“version”:”1.1″,”math”:”r→(t)=t2,et,sint”}. Part (a) (5 points) Find limt→0r→(t){“version”:”1.1″,”math”:”limt→0r→(t)”} Part (b) (5 points) Find the derivative of r→(t){“version”:”1.1″,”math”:”r→(t)”} Part (c) (5 points) Find ∫r→(t)dt{“version”:”1.1″,”math”:”∫r→(t)dt”} Problem 6. (10 points) Find the arch length of the curve   r→(t)=2sint,2cost,t{“version”:”1.1″,”math”:”  r→(t)=2sint,2cost,t”} with 1≤t≤3{“version”:”1.1″,”math”:”1≤t≤3″}. Problem 7. (15 points) Consider the curve r→(t)=t,t2,4{“version”:”1.1″,”math”:”r→(t)=t,t2,4″}. Find the unit tangent vector T→{“version”:”1.1″,”math”:”T→”} and the curvature at t=0{“version”:”1.1″,”math”:”t=0″}. Once you are done, take photos of your handwritten work, convert it into a pdf, and then send your work to your instructor within ten minutes after you hit the submit button on the exam. You can either sent it to the instructor via D2L messages or to the following email address            collier.gaiser@ccaurora.edu