1.Calculate the given quantity if a = , b = , c = < 3, 4

1.Calculate the given quantity if a = < 0, 2, 1 >, b = < -1, -2, 1 >, c = < 3, 4

ID: 3372578 • Letter: 1

1.Calculate the given quantity if a = < 0, 2, 1 >, b = < -1, -2, 1 >, c = < 3, 4, 1 >

a) Dot product of a and b

b) | a |

c) A unit vector in the direction of a

d) b x c

2. For the line segment going from P0(2, 1, -3) to the point P1(5, -2, 0), find the vector equation, r(t), for the line segment.

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/or saddle points for the given function.

f(x,y)= x^2=12y+y^3

6. What are the spherical coordinates of the point whose rectangular coordinates are

(x = sqrt(3)/2 y = 1/2 , z = sqrt(3) )?

p= _____ (theta)= ______ phi=______

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