Need To Remember Solving These exercises! - Help!

It's been quite a while since i last have tried to solve these exercises for college.

Can someone try to re-explain them to me along with the progressive solutions and calculus, please?

Here they are

Quote:

1) Let B={e1=(2,1,3), e2=(1,0,1), e3=(1,1,1)}, find:

a) B- Basis of the vector space R(to the third)

b) expression of vector x=(2,0,3) with respect to basis B

Quote:

2) Let A(1,0,0), B(0,3,0), C(0,0,2). Calculate the volume of the tetrahedron OABC and it's altitude from A.

Quote:

3) Let A,B,C - as above :

a) equation of plane (ABC)

b)the projection of 0(0,0,0) onto the plane (ABC)

Quote:

4) Find the equation of the surface obtained by rotating the curve :

(C)-|y=sinx

|z=0 around (d)=0x

Quote:

5)Determine the tangent and the normal line to {x=4-sint and {y=1-cost, t belonging to [0, 2π] at A(t=π/2)

and:

Quote:

6) Determine the curvature and the torsion of

(C)r(t)= costi(vector)+sintj(vector)+tk(vector) at (0,1,π/2) t belonging to R

(Nerd)