Suppose that vector a + radical 3 vector B is perpendicular to 4 vector A-3 radical 3 vector B, 2 vector a + radical 3 vector B is perpendicular to vector a-radical 3 vector B, And the vectors a and B are not equal to 0, find the angle between a and B

Suppose that vector a + radical 3 vector B is perpendicular to 4 vector A-3 radical 3 vector B, 2 vector a + radical 3 vector B is perpendicular to vector a-radical 3 vector B, And the vectors a and B are not equal to 0, find the angle between a and B

(vector a + radical 3 vector b) times (4 vector A-3 radical 3 vector b) = 4A ^ 2 + radical 3ab-9b ^ 2 = 0
(2 vector a + radical 3 vector b) * (vector a-radical 3 vector b) = 2A ^ 2-radical 3ab-3b ^ 2 = 0
So | a | ^ 2 = 2 | B | ^ 2
Cos (a, b) = a * B / | a | B | = B ^ 2 / radical 3 * radical 2 | B | ^ 2 = radical 6 / 6
Artcos (radical 6 / 6)