Let v₁ and v2 be the 4 x 1 columns of MT and suppose P is the plane through the origin with v₁ and v₂ as direction vectors. (a) Find which of v₁ and v2 is longer in length and then calculate the angle between ₁ and v2 using the dot product method. [3 marks] (b) Use Gram-Schmidt to find e2, the vector perpendicular to v₁ in P, express e2 with integer entries, and check that e₁e2 = 0. [3 marks] 1 (c) Now take v3 := 0- and use 0 Gram-Schimdt again to find an ez is orthogonal to e₁ and e2 but is in the hyperplane with v₁, v2 and v3 as a basis. [4 marks] 3 1 -1 1 -5 5 5 2 -3