It is known that vector a = (1,2), vector b = (- 2, n) and the angle between vector a and B is 45 degrees (1) Finding the vector b (2) If the vector C and B are in the same direction, and C-A is perpendicular to a, find C

It is known that vector a = (1,2), vector b = (- 2, n) and the angle between vector a and B is 45 degrees (1) Finding the vector b (2) If the vector C and B are in the same direction, and C-A is perpendicular to a, find C

(1) ∵ a · B = | a | B | cos (θ), θ is the angle between a and B ∵ - 2 + 2n = √ 5 * √ (4 + n & sup2;) * (√ 2) / 2 ----- ① the two sides of the square are reduced to: 8 (n-1) & sup2; = 5 (4 + n & sup2;) ---- ② so n = 6 or - 2 / 3 because of the square, formula ② also calculates the included angle of 145 degrees, substituting formula ① to verify