question 1 and 2

1. [25 marks] In Re with the usual dot product. a) Find the angle between the vectors and : b) Find the distance from c) Find the vector on the line ( = itER3 which is closest to and compute the distance from this vector to d) Show that all vectors in the plane P = NCH :x+y+ = =0 are perpendicular to e) Find the shortest distance from to the plane P (hint: draw a picture and use part (c)). 2. [15 marks] In CR[-1, 1] with inner product (f(x), g(x)) = [, f(x)g(x) dr. a) Find the angle between f(x) = e and g(x) = 1 b) Find the distance from f(x) = el to g(x) = 1 c) Find the constant function which is closest to f(x) = er on [-1, 1] (in the sense that _ [m -e(2 dx is minimized) and compute the distance from this constant function to f(x) = er