1.Calculate the given quantity if a = < 0,2, 1 >, b = < -1, -2, 1 >, c = < 3, 4, 1>
a) Dot product ofa and b
b)| a |
c) A unit vectorin the direction of a
d) b xc
2. For the line segment going fromP0(2, 1, -3) to the pointP1(5, -2, 0), find the vectorequation, r(t), for the linesegment.
3. Find the length of the curve r(t) =< cos(3t), sin(3t), 5t > from t = 0 to t = 1.
4. For the curve r(t) = < cos(5t),sin(5t),12t >
(a) The Unit Tangent vector, T(t)= r'(t) /|r'(t)|
(b) The Unit Normal vector, N(t) = T'(t) /|T'(t)|
5. Find and classify all local extrema and/orsaddle points for the given function.
f(x,y)= x^2=12y+y^3
6. What are the sphericalcoordinates of the point whose rectangular coordinates are
(x = sqrt(3)/2 y = 1/2 , z = sqrt(3) )?
p=_____ (theta)=______ phi=______
1.Calculate the given quantity if a = < 0,2, 1 >, b = < -1, -2, 1 >, c = < 3, 4, 1>
a) Dot product ofa and b
b)| a |
c) A unit vectorin the direction of a
d) b xc
2. For the line segment going fromP0(2, 1, -3) to the pointP1(5, -2, 0), find the vectorequation, r(t), for the linesegment.
3. Find the length of the curve r(t) =< cos(3t), sin(3t), 5t > from t = 0 to t = 1.
4. For the curve r(t) = < cos(5t),sin(5t),12t >
(a) The Unit Tangent vector, T(t)= r'(t) /|r'(t)|
(b) The Unit Normal vector, N(t) = T'(t) /|T'(t)|
5. Find and classify all local extrema and/orsaddle points for the given function.
f(x,y)= x^2=12y+y^3
6. What are the sphericalcoordinates of the point whose rectangular coordinates are
(x = sqrt(3)/2 y = 1/2 , z = sqrt(3) )?
p=_____ (theta)=______ phi=______
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