Nearest point to a line. let a and b be different n-vectors. the line passing through a and b is given by the set of vectors of the form (1−θ)a+θb, where θ is a scalar that determines the particular point on the line. (see page 18.) let x be any n-vector. find a formula for the point p on the line that is closest to x. the point p is called the projection of x onto the line. show that (p − x) ⊥ (a − b), and draw a simple picture illustrating this in 2-d. hint. work with the square of the distance between a point on the line and x, i. e., ∥(1 − θ)a + θb − x∥2. expand this, and minimize over θ.