1) Consider two vectors u = <t, 2, t - 1> and v = <3, t + 1, 4> where t is a parameter.

(a) Find all values of t such that u + v = 0
(b) Find all values of t such that u and v are orthogonal.
(c) Find all values of t such that u  v = 0.

2) Consider the plane x + y + z = 0 and a sphere x^2 + y^2 + z^2 - 8x - 6y - 10z + 49 = 0.

(a) Find the center and the radius of the sphere.
(b) Is the point (4, 3, 4) on the sphere?
(c) Find the ( minimum ) distance between the sphere and the plane

3) Consider a particle with position given by the vector function r(t) = <e^t, e^-t, t(sqrt 2)>

(a) Find the distance between the particle's position at time t = 0 and t = 1.
(b) Find the speed of the particle at t = 0.
(c) Find the distance traveled by the particle from time t = 0 to t = 1.
(d) Find the acceleration vector of the particle at t = 1

4) Consider the space curve given by the vector function r(t) = <sin 2t, 3t, cos 2t>

(a) Find the unit tangent vector T(t).
(b) Find parametric equations of the tangent line to the curve at t = 0.
(c) Find the unit normal vector N(t).
(d) Find the curvature at t = 0.

Do you have a problem with any of these in particular or do you want someone to do all of them for you ?

These are just review problems and I want to refresh my head. All I actually need help with is,

1)A,B and C
2) B and C
3)A and C

No one?

a. u+v
b. dot product=0
c. *? so multiply terms

actually, this just shows you're completely lazy
what, 2 months into courses and don't know how to do this?
most of this is still algebra , just do what the question asks

This post was edited by saber_x3 on Feb 26 2014 12:06pm

actually I think c is cross product, so its not a simple multiplication, see the formula here http://tutorial.math.lamar.edu/Classes/CalcII/CrossProduct.aspx

This post was edited by m0hawk on Feb 26 2014 12:24pm

bud this looks critical, I still have a few semesters to go before taking this course, are you a engineering major as well?

yes, parallel would fit the scheme much better