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MAT 21D Final Exam Questions With Multiple Choices & Verified Answers. $12.99   Add to cart

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MAT 21D Final Exam Questions With Multiple Choices & Verified Answers.

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  • Course
  • MAT.
  • Institution
  • MAT.

Arc length in space - correct answer unit tangent vector formula - correct answer Find arc length parametrization - correct answer 1. find the arc length...

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  • August 14, 2024
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  • 2024/2025
  • Exam (elaborations)
  • Questions & answers
  • MAT.
  • MAT.
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RealGrades
MAT 21D Final

Arc length in space - correct answer



unit tangent vector formula - correct answer



Find arc length parametrization - correct answer 1. find the arc length (s =xt)

2. solve for t

3. plug back into position equation to get r(s)



Formula for curvature - correct answer



unit normal vector formula - correct answer



curvature of plane curve - correct answer



tangential component of acceleration - correct answer d/dt | v(t) |



normal component of acceleration - correct answer sqrt[ |a|^2 - (aT)^2 ]



scalar line integrals - correct answer the integrand is a function of more than
one variable

- domain of integration is a curve in a plane/space



line integrals of line segment C - correct answer r(t) = (1-t)<x,y,z> + (t)<x,y,z>



Vector Line Integral - correct answer ∫Px' + Qy' + Rz'

, path independent and conservative - correct answer Let F be a vector field
defined on an open region D in space.



Suppose that for any two points A and B in D, the path C from A to B in D is the same over all paths from
A to B.



Find the work done by F in moving an object along a smooth curve C - correct answer
If F is a conservative field:



W = f(B) - f(A)

curlF = 0



W = ∫F(r(t)) * r'(t)



Test for Exactness - correct answer



vectors are perpendicular if: - correct answer u1v1 + u2v2 + u3v3 = 0 (dot
product)



proj of u onto v - correct answer



cross product - correct answer (u2v3 - u3v2)i + (u1v3 - u3v1)j + (u1v2 - u2v1)k



gradient vector - correct answer



When are two vectors parallel? - correct answer the cross product is 0



unit binomial vector - correct answer cross product of tangent and normal



Curl of a vector field - correct answer (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k

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