Given vector a = (1,2), vector b = (- 2, n), the angle between vector a and B is 45 ° (1) find B (2) if C and B are in the same direction, and C-A ⊥ a, find C

Given vector a = (1,2), vector b = (- 2, n), the angle between vector a and B is 45 ° (1) find B (2) if C and B are in the same direction, and C-A ⊥ a, find C

Let the angle between vector a and vector b be a
Cosa = 1 * (- 2) + 2n / radical 5 * radical (4 + n ^) = radical 2 / 2
N = 6 or - 2 / 3
So B = (- 2,6)
Let C = (x, y)
c-a=(1-x,2-y)
Because C-A ⊥ a
Then 1-x + 2 (2-y) = 0
Because C and B have the same direction, that is, x = - 3Y
So x = 3, y = - 1
c=(3,-1)