In the plane rectangular coordinate system, points a (1,1), B (4,2), C (2,3). 1 seek the coordinates of vector AB (with arrow) + AC (with arrow), 2 seek the angle α of vector AB (with arrow) and AC (with arrow)

In the plane rectangular coordinate system, points a (1,1), B (4,2), C (2,3). 1 seek the coordinates of vector AB (with arrow) + AC (with arrow), 2 seek the angle α of vector AB (with arrow) and AC (with arrow)

The vector AB is equal to (3,1) and the vector AC is equal to (1,2), so the coordinates of AB + AC are equal to (4,3). Second, according to the vector angle formula: cos angle = a vector point multiplied by B vector / (module of a vector * module of B vector), cos α = (3 * 1 + 1 * 2) divided by (root 10 * root 5) = 2 / 2 root 2, so the angle α = 45 degrees