Hi, guys I need some help. I've checked in my calc. book and cant find a similar problem. This is the problem:
The velocity vector of a particle moving in space equals v(t) = 2t i + 2t j + t k at any
time t.
(a) At the time t = 4, this particle is at the point (0; 5; 4). Find an equation of the
tangent line to the curve at the time t = 4.
(b) Find the length of the arc traveled from time t = 2 to time t = 4.
(c) Find a vector function which represents the curve of intersection of the cylinder
x^2 + y^2 = 1 and the plane x + 2y + z = 4.
I'm just trying to do part a. I just dont know where to start. Am I supposed to change the given velocity vector function to the position vector function, then you the formula T(t)= (r'(t)/|r'(t)|)? Then I just fill in t=4? The given point is through me off. I think this is the way to do it, but this is only 1 of 2 questions on homework, so I cant afford to get it wrong. Please just confirm this for me, so i can start working. I posted the other parts, because after I solve them I will problem post my answers to see if they are right or not. Thank you!
The velocity vector of a particle moving in space equals v(t) = 2t i + 2t j + t k at any
time t.
(a) At the time t = 4, this particle is at the point (0; 5; 4). Find an equation of the
tangent line to the curve at the time t = 4.
(b) Find the length of the arc traveled from time t = 2 to time t = 4.
(c) Find a vector function which represents the curve of intersection of the cylinder
x^2 + y^2 = 1 and the plane x + 2y + z = 4.
I'm just trying to do part a. I just dont know where to start. Am I supposed to change the given velocity vector function to the position vector function, then you the formula T(t)= (r'(t)/|r'(t)|)? Then I just fill in t=4? The given point is through me off. I think this is the way to do it, but this is only 1 of 2 questions on homework, so I cant afford to get it wrong. Please just confirm this for me, so i can start working. I posted the other parts, because after I solve them I will problem post my answers to see if they are right or not. Thank you!