b) The tangent subspace Wp at p ES is the plane through 0 with normal vector p. Find an explicit formula in terms of a, b, c, x, y, z for the projection Tp(x) of a vector x = (x, y, z) = R³ to the tangent subspace Wp.

Find a vector parametrization of the line through P = (0, -3, -2) in the direction V = (6, 4, 1) r(t) = ( 1 1 + + - t) j+ t) k t) i+ I +

a) Find a point-normal form of the equation of the plane passing through the point P =(4,-2,1) and perpendicular to the vector n = (4,2,-1). b) Find the vector component of u=(1,4,-1) along a=(5,-2,1) and the vector component of u orthogonal to a.

5. Let C be the portion of the parabola y = x², oriented from the starting point (0, 0) towards the end point (3,9). Find the unit tangent vector T and the unit normal vector n to C at the point (1, 1).