Calculus 3 Practice Exam 3 - Math 209 Exam 3 Practice 1 Find parametric equations for the line containing the points P(1 2 4 and Q(3 0 7 2 Find the

Calculus 3 Practice Exam 3 - Math 209 Exam 3 Practice 1...

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Math 209Exam 3Practice1. Find parametric equations for the line containing the pointsP(1,2,4) andQ(3,0,7).2. Find the equation of the plane containing the point (3,-1,4) with normal vector2,5,6 .3. FindZ104t,5,12t3fidtFor the remaining problems, letr(t) =4t,-3 sin(t),3 cos(t) .4. Find the length of the curve betweent= 0 andt=π2.5. Find the unit tangent vectorTatt=π2.6. Find the unit normal vectorNatt=π2.7. Find the unit binormal vectorBatt=π2.8. Find the curvatureκatt=π2.9. Find the velocity and acceleration vectors att=π2.10. Find the tangential and normal components of the acceleration vector att=π2Bonus: EvaluateZ1-1et, e-t,1fidt
Math 209Exam 3PracticeSolutions1.-→PQ=2,-2,3 , sor=1,2,4 + 2,-2,3t=1 + 2t,2-2t,4 + 3tThus,x= 1 + 2t,y= 2-2tz= 4 + 3t.2. 2(x-3) + 5(y+ 1) + 6(z-4) = 0, which reduces to 2x+ 5y+ 6z= 25.3.Z104t,5,12t3fidt=£›2t2,5t,3t4fi/10=2,5,34.r=4,-3 cost,-3 sint, so|r|= 5, thusL=Zπ/205dt= 5π/2.5.T=r

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