Plane vector set application. I'm in a hurry~ In △ ABC, D, e and F are the middle points of edge AB, BC and Ca respectively, and G is its center of gravity. Given that the coordinates of point D are (1,2), the coordinates of point e are (3,5), and the coordinates of point F are (2,7), find the coordinates of a, B, C and G

Plane vector set application. I'm in a hurry~ In △ ABC, D, e and F are the middle points of edge AB, BC and Ca respectively, and G is its center of gravity. Given that the coordinates of point D are (1,2), the coordinates of point e are (3,5), and the coordinates of point F are (2,7), find the coordinates of a, B, C and G

Let the coordinates of a, B, C and G be (XA, ya) (XB, Yb) (XC, YC) (XG, YG, D, e and F are the midpoint of edge AB, BC and Ca respectively, so (XA + XB) / 2 = 1 (Ya + Yb) / 2 = 2 (XB + XC) / 2 = 3 (Yb + YC) / 2 = 5 (XA + XC) / 2 = 2 (Ya + YC) / 2 = 7. By solving the above equations, we can get the coordinates of g of a, B and C

A plane vector problem
Known vector a = (3,2) vector b = (- 1,0)
Find the cosine value of the angle α between vector 3a-2b and vector B
Because I'm not right

The inner product of 3a-2b and B is = - 11 * 1 + 0 = - 11
The modules of 3a-2b and B are
(11 ^ 2 + 6 ^ 2) and √ 1
The cosine of the angle between two vectors is equal to the inner product divided by the product of two vector modules
Cosine of angle between two vectors = - 11 / √ 157
Angle between two vectors = arccos (11 / √ 157)

There are three mathematical multiple choice questions (about plane vector) in question, please explain in detail
1. Given that | B vector | = 3, the projection of a vector in the direction of B vector is 2 / 3, then a vector · B vector is ()
A 3 B 2/9 C 2 D 1/2
2. In △ ABC, AB vector = a vector, BC vector = B vector, and a vector · B vector > 0, then △ ABC is ()
A acute triangle b right triangle C obtuse triangle D isosceles right triangle
3. A (1,2), B (2,3), C (2,0), so △ ABC is ()
A right triangle B acute triangle C obtuse triangle D unequal triangle

In the first question, we should consider the concept of product of quantity. The projection of a vector in the direction of B vector is 2 / 3 → let the angle between two vectors be θ. Then | a | * cos θ = 2 / 3, | a * b = | a | * B | * cos θ = 2