Need help with these problems with steps
1. Find the parametric equations for the following curves:
A. The line segment from P = (9; 8; 5) to Q = (13;-2; 0).
B. x^2 + y^2 = 9 for only positive x values.
2. Find the vector valued function describing the curves of intersection of the pairs of surfaces. Then draw the two surfaces together in the space provided.
A. The parabaloid y = x^2 + z^2 and the parabolic cylinder z = x^2.
B. The cylinder x^2 + y^2 = 1 and the parabolic cylinder z = x^2.
3. If a particle has an initial position of ~r(0) = i^ - 2j^ and its velocity is given by the vector function ~v(t) = < 2e^(2t) ; 3t^2- 1; t^3> , find the particles position function and acceleration function.
4. Find the tangent line to the curve ~r(t) = < 3ln(t) , 2t -3 , 1/t> at t= 1
5. If a particle follows the path dened by ~r(t) = < 2t^(3/2) ; 2t+1; sort(5)t > and starts at t = 0, at what time will the particle have traveled a total of 14 units?
6. Let ~r(t) = < t; t; 2 -t^2>. Find the curvature when t = 0, denoted by K(0).
7.write vector valued function for the paths from the north pole to south pole of the unit sphere below:
A. along the intersection with the plane x=0 where y>= 0.
B. along intersection with the plane y=x where x,y >= 0
C. along a path that curves the sphere once counterclockwise as views in the xy-plane.
9. r(t)= ( (1/3)t^3, (1/sqrt(2)), t )
A. find the length t=1
B. find the curvature when t=2
c.find the unite tangent, unit normal and unit bi-normal vector for the function at the point where t=1